The generator matrix

 1  0  1  1  1 X^3+X^2+X  X  1  1 X^3  1  1 X^2  1  1  1 X^2+X  1  1 X^3+X^2  1 X^3+X  1  1  1  1  1 X^3+X  1  0  1  1  1  1  1 X^3 X^3+X^2+X  1  1  1  1 X^2 X^3+X  1 X^3+X X^3  1  1  1  1  X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  1 X^2  1  1
 0  1 X+1 X^2+X X^3+X^2+1  1  1 X^3+X^2 X^2+X+1  1 X^3+X  1  1 X^3 X+1 X^3+X^2+X  1 X^3+X^2+X+1 X^2  1  X  1 X+1 X^3+X^2+X+1 X^2+1 X^3+1  0  1 X^2+1  1 X^3+X^2+X X^3+X+1 X^2 X^3+X^2+1 X^2+X  1  1 X^3+1 X^3+X^2 X^3+X X^2+X  1  1 X^3+X+1  1  1 X^3  1  0  X X^2 X^3+X X^3 X^2 X^3+X^2 X^3+X  X X^2+X X^2 X^2+X X^2 X^2+X X^2 X^2+X X^3+X X^3 X^3 X^3+X^2+X  1 X^3+X+1  X X^3+X X^3+X
 0  0 X^2  0 X^3+X^2 X^2 X^2  0 X^3+X^2 X^3+X^2  0 X^2 X^3+X^2 X^2 X^3 X^3+X^2  0 X^3 X^2  0 X^3+X^2  0 X^3 X^3  0 X^3  0  0 X^3  0 X^3+X^2 X^2 X^2 X^3+X^2 X^3 X^2 X^2  0  0 X^3 X^2 X^2 X^3 X^2 X^2 X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^3 X^2 X^2  0 X^3  0  0 X^3 X^3 X^3 X^3+X^2 X^3+X^2  0  0 X^2 X^2 X^3 X^3 X^3 X^3+X^2 X^2  0 X^3
 0  0  0 X^3  0  0  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3  0 X^3 X^3  0  0 X^3  0  0 X^3 X^3  0 X^3  0 X^3  0 X^3  0  0  0 X^3  0 X^3  0  0  0 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3  0  0  0 X^3 X^3  0 X^3  0  0 X^3  0  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3  0  0  0
 0  0  0  0 X^3  0 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0 X^3  0  0  0 X^3  0 X^3 X^3 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 X^3 X^3 X^3  0  0  0  0 X^3  0 X^3 X^3  0 X^3 X^3  0  0  0  0  0  0 X^3  0 X^3 X^3  0  0 X^3 X^3 X^3  0 X^3 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+160x^68+252x^69+426x^70+428x^71+562x^72+592x^73+418x^74+384x^75+486x^76+244x^77+80x^78+20x^79+23x^80+2x^82+12x^84+2x^86+2x^88+2x^108

The gray image is a linear code over GF(2) with n=584, k=12 and d=272.
This code was found by Heurico 1.16 in 0.609 seconds.