The generator matrix

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

generates a code of length 73 over Z2[X]/(X^4) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+94x^69+265x^70+314x^71+251x^72+308x^73+242x^74+212x^75+189x^76+78x^77+69x^78+16x^79+5x^80+2x^95+1x^100+1x^104

The gray image is a linear code over GF(2) with n=584, k=11 and d=276.
This code was found by Heurico 1.16 in 0.438 seconds.