The generator matrix

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

generates a code of length 73 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+160x^69+91x^70+374x^71+308x^72+310x^73+291x^74+276x^75+40x^76+84x^77+33x^78+54x^79+2x^80+22x^81+1x^82+1x^128

The gray image is a code over GF(2) with n=584, k=11 and d=276.
This code was found by Heurico 1.16 in 0.453 seconds.