The generator matrix

 1  0  1  1  1 X^2+X  1 X^3+X^2  1  1  1 X^3+X  1  1 X^3  1 X^3+X^2+X  1  1 X^2  1  X  1  1  1  1  1 X^3+X^2  1  1 X^2+X  1  1 X^3+X^2+X  1  0  1  X  1  1  1  1 X^3  X  1  1  1  1 X^2  1  1  1  1  1  1  1  1  1  1  1  1  1  X  0  1  1  1  1  1  X  1  1  1  X  1  1  1  1  1  1  1  1  X  1  0  1 X^3+X^2+X X^3  1 X^3+X^2  1
 0  1 X+1 X^3+X^2+X X^3+X^2+1  1  X  1 X^2+X+1 X^3  1  1 X^2 X+1  1 X^2+1  1 X^3+X^2 X^3+X^2+X+1  1 X^3+1  1  0 X^3+X^2 X^2+X X^3+X X+1  1 X^3+X X^2+1  1 X^2+X X^3+X+1  1 X^3+1  1 X^2+X  1 X^3  1 X^3+X^2+X+1 X^3+X^2  1  1 X^3+X^2+1 X^3+X X^3+X^2 X^2+X+1  1  0 X^3+X^2+X X^2+X  0  0 X^3+X X^2 X^3+X X^3+X^2  X X^3+X  0 X^3+X^2  0  1 X^2+X X+1 X^2+1 X^3+X^2 X^2+X  1 X^3+X^2+X X^2+X  0 X^3+X^2 X^3+X X^3 X^2+X+1 X^3+X^2+X+1 X^3+X^2+X X^2+1 X^2+1 X^3+X^2+1  1 X^3  1 X^3+X^2+X  1  1 X^3+1  1  0
 0  0 X^2 X^2 X^3+X^2  0 X^3+X^2  0 X^2 X^2 X^3+X^2  0 X^3+X^2 X^3 X^2 X^3 X^2  0 X^3 X^2 X^3 X^2  0  0  0 X^3 X^3  0  0 X^3  0  0 X^2 X^2 X^3  0 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^3  0 X^2  0 X^3+X^2 X^2 X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^2 X^2  0 X^3 X^2  0 X^3+X^2 X^3+X^2 X^3+X^2  0 X^3 X^3 X^2 X^3 X^2 X^3+X^2  0 X^3 X^2 X^2 X^3+X^2 X^3+X^2 X^3  0 X^3+X^2 X^2 X^3+X^2 X^3  0 X^3  0 X^3+X^2 X^3 X^3 X^3+X^2 X^3  0  0 X^3 X^3
 0  0  0 X^3  0 X^3 X^3 X^3 X^3  0 X^3  0  0 X^3  0 X^3  0  0  0 X^3  0 X^3 X^3 X^3  0 X^3  0  0 X^3  0  0  0  0 X^3 X^3 X^3 X^3  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3  0 X^3  0 X^3  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0  0  0  0  0 X^3 X^3  0  0  0 X^3 X^3  0 X^3  0 X^3  0 X^3 X^3  0 X^3  0  0  0 X^3  0  0 X^3 X^3 X^3 X^3
 0  0  0  0 X^3  0 X^3 X^3 X^3 X^3  0 X^3  0  0  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0  0  0 X^3 X^3  0  0  0 X^3 X^3  0  0  0  0 X^3 X^3  0 X^3 X^3 X^3 X^3  0 X^3  0 X^3  0  0  0 X^3 X^3  0 X^3  0 X^3 X^3 X^3  0 X^3  0 X^3 X^3  0  0 X^3  0 X^3  0 X^3 X^3  0  0 X^3 X^3 X^3  0  0 X^3  0  0  0 X^3 X^3 X^3  0 X^3 X^3  0  0

generates a code of length 91 over Z2[X]/(X^4) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+182x^86+356x^87+483x^88+338x^89+458x^90+594x^91+408x^92+300x^93+465x^94+264x^95+126x^96+62x^97+43x^98+2x^99+5x^100+2x^101+1x^102+2x^109+2x^110+1x^130+1x^132

The gray image is a linear code over GF(2) with n=728, k=12 and d=344.
This code was found by Heurico 1.16 in 1.17 seconds.