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

generates a code of length 92 over Z2[X]/(X^4) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+224x^86+120x^87+324x^88+248x^89+500x^90+408x^91+592x^92+408x^93+474x^94+232x^95+190x^96+104x^97+114x^98+8x^99+97x^100+8x^101+22x^102+8x^104+10x^106+3x^108+1x^152

The gray image is a linear code over GF(2) with n=736, k=12 and d=344.
This code was found by Heurico 1.16 in 2.39 seconds.