The generator matrix

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

generates a code of length 94 over Z2[X]/(X^4) who´s minimum homogenous weight is 89.

Homogenous weight enumerator: w(x)=1x^0+198x^89+225x^90+526x^91+415x^92+696x^93+365x^94+456x^95+278x^96+442x^97+192x^98+150x^99+39x^100+66x^101+11x^102+20x^103+1x^104+2x^105+5x^106+2x^108+2x^109+2x^113+1x^130+1x^138

The gray image is a linear code over GF(2) with n=752, k=12 and d=356.
This code was found by Heurico 1.16 in 1.34 seconds.