The generator matrix

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

generates a code of length 91 over Z4[X]/(X^2+2) who�s minimum homogenous weight is 87.

Homogenous weight enumerator: w(x)=1x^0+86x^87+291x^88+224x^89+534x^90+236x^91+170x^92+120x^93+88x^94+46x^95+185x^96+40x^97+8x^98+16x^99+1x^112+1x^114+1x^130

The gray image is a code over GF(2) with n=728, k=11 and d=348.
This code was found by Heurico 1.16 in 0.954 seconds.