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

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+66x^89+72x^90+98x^91+203x^92+206x^93+170x^94+80x^95+37x^96+42x^97+18x^98+14x^99+6x^100+6x^101+2x^102+2x^114+1x^132

The gray image is a linear code over GF(2) with n=744, k=10 and d=356.
This code was found by Heurico 1.16 in 0.766 seconds.