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

generates a code of length 94 over Z2[X]/(X^4) who´s minimum homogenous weight is 89.

Homogenous weight enumerator: w(x)=1x^0+204x^89+760x^90+1070x^91+1199x^92+946x^93+919x^94+758x^95+605x^96+472x^97+418x^98+204x^99+265x^100+164x^101+92x^102+60x^103+24x^104+22x^105+2x^106+4x^107+1x^110+2x^116

The gray image is a linear code over GF(2) with n=752, k=13 and d=356.
This code was found by Heurico 1.16 in 18.2 seconds.