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

generates a code of length 97 over Z2[X]/(X^4) who´s minimum homogenous weight is 90.

Homogenous weight enumerator: w(x)=1x^0+52x^90+106x^91+208x^92+260x^93+380x^94+338x^95+546x^96+456x^97+515x^98+322x^99+338x^100+176x^101+183x^102+80x^103+52x^104+26x^105+11x^106+16x^107+6x^108+8x^109+8x^110+2x^111+1x^112+2x^113+2x^114+1x^158

The gray image is a linear code over GF(2) with n=776, k=12 and d=360.
This code was found by Heurico 1.16 in 2.06 seconds.