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

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+70x^86+248x^87+284x^88+448x^89+367x^90+490x^91+431x^92+532x^93+301x^94+324x^95+229x^96+200x^97+61x^98+22x^99+29x^100+16x^101+9x^102+20x^103+8x^104+4x^105+1x^116+1x^148

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 1.33 seconds.