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

generates a code of length 95 over Z2[X]/(X^4) who´s minimum homogenous weight is 88.

Homogenous weight enumerator: w(x)=1x^0+29x^88+134x^89+159x^90+260x^91+314x^92+436x^93+634x^94+522x^95+398x^96+366x^97+325x^98+164x^99+105x^100+60x^101+48x^102+66x^103+14x^104+24x^105+16x^106+12x^107+4x^109+1x^110+2x^112+1x^118+1x^156

The gray image is a linear code over GF(2) with n=760, k=12 and d=352.
This code was found by Heurico 1.16 in 1.94 seconds.