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

generates a code of length 93 over Z2[X]/(X^4) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+68x^86+70x^87+199x^88+164x^89+357x^90+254x^91+830x^92+350x^93+792x^94+262x^95+305x^96+88x^97+149x^98+44x^99+66x^100+30x^101+38x^102+8x^103+3x^104+8x^105+1x^106+2x^107+4x^108+2x^110+1x^162

The gray image is a linear code over GF(2) with n=744, k=12 and d=344.
This code was found by Heurico 1.16 in 1.8 seconds.