The generator matrix

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

generates a code of length 96 over Z2[X]/(X^4) who´s minimum homogenous weight is 91.

Homogenous weight enumerator: w(x)=1x^0+254x^91+775x^92+1084x^93+967x^94+1068x^95+941x^96+816x^97+531x^98+568x^99+305x^100+260x^101+212x^102+192x^103+97x^104+40x^105+64x^106+6x^107+8x^108+1x^110+1x^120+1x^122

The gray image is a linear code over GF(2) with n=768, k=13 and d=364.
This code was found by Heurico 1.16 in 7.08 seconds.