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

generates a code of length 97 over Z2[X]/(X^4) who´s minimum homogenous weight is 91.

Homogenous weight enumerator: w(x)=1x^0+90x^91+228x^92+294x^93+331x^94+424x^95+520x^96+536x^97+483x^98+384x^99+258x^100+168x^101+108x^102+80x^103+89x^104+52x^105+28x^106+10x^107+6x^109+1x^110+4x^111+1x^162

The gray image is a linear code over GF(2) with n=776, k=12 and d=364.
This code was found by Heurico 1.16 in 1.56 seconds.