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

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+92x^69+164x^70+284x^71+413x^72+364x^73+307x^74+172x^75+58x^76+48x^77+64x^78+56x^79+16x^80+8x^81+1x^138

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 14.4 seconds.