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

generates a code of length 73 over Z2[X]/(X^4) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+104x^68+256x^70+288x^71+236x^72+480x^73+128x^74+224x^75+104x^76+32x^77+128x^78+66x^80+1x^128

The gray image is a linear code over GF(2) with n=584, k=11 and d=272.
This code was found by Heurico 1.16 in 0.484 seconds.