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

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+186x^68+88x^70+96x^71+530x^72+320x^73+416x^74+96x^75+226x^76+8x^78+68x^80+12x^84+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 4.28 seconds.