The generator matrix

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

generates a code of length 96 over Z2[X]/(X^4) who´s minimum homogenous weight is 90.

Homogenous weight enumerator: w(x)=1x^0+299x^90+950x^91+1250x^92+1638x^93+2102x^94+1746x^95+1673x^96+1474x^97+1396x^98+1270x^99+921x^100+572x^101+515x^102+282x^103+91x^104+98x^105+49x^106+22x^107+15x^108+10x^109+5x^110+2x^114+2x^115+1x^120

The gray image is a linear code over GF(2) with n=768, k=14 and d=360.
This code was found by Heurico 1.16 in 12.4 seconds.