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

generates a code of length 94 over Z2[X]/(X^4) who´s minimum homogenous weight is 88.

Homogenous weight enumerator: w(x)=1x^0+112x^88+192x^89+344x^90+378x^91+239x^92+684x^93+354x^94+674x^95+205x^96+298x^97+230x^98+150x^99+135x^100+32x^101+19x^102+14x^103+12x^104+10x^105+12x^106+1x^158

The gray image is a linear code over GF(2) with n=752, k=12 and d=352.
This code was found by Heurico 1.16 in 1.42 seconds.