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

generates a code of length 93 over Z2[X]/(X^4) who´s minimum homogenous weight is 89.

Homogenous weight enumerator: w(x)=1x^0+128x^89+63x^90+260x^91+193x^92+808x^93+190x^94+192x^95+61x^96+120x^97+3x^98+28x^99+1x^180

The gray image is a linear code over GF(2) with n=744, k=11 and d=356.
This code was found by Heurico 1.16 in 1.06 seconds.