The generator matrix

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

generates a code of length 93 over Z2[X]/(X^4) who´s minimum homogenous weight is 88.

Homogenous weight enumerator: w(x)=1x^0+318x^88+96x^89+712x^90+192x^91+537x^92+448x^93+590x^94+192x^95+552x^96+96x^97+276x^98+61x^100+22x^102+1x^120+2x^132

The gray image is a linear code over GF(2) with n=744, k=12 and d=352.
This code was found by Heurico 1.16 in 1.28 seconds.