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

generates a code of length 95 over Z2[X]/(X^4) who´s minimum homogenous weight is 89.

Homogenous weight enumerator: w(x)=1x^0+96x^89+293x^90+230x^91+363x^92+370x^93+612x^94+388x^95+543x^96+304x^97+380x^98+142x^99+127x^100+42x^101+77x^102+56x^103+22x^104+36x^105+12x^106+1x^110+1x^154

The gray image is a linear code over GF(2) with n=760, k=12 and d=356.
This code was found by Heurico 1.16 in 1.47 seconds.