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

generates a code of length 65 over Z2[X]/(X^4) who´s minimum homogenous weight is 59.

Homogenous weight enumerator: w(x)=1x^0+92x^59+167x^60+194x^61+298x^62+448x^63+625x^64+642x^65+543x^66+436x^67+224x^68+120x^69+132x^70+62x^71+26x^72+34x^73+16x^74+12x^75+9x^76+2x^77+2x^78+6x^79+4x^80+1x^98

The gray image is a linear code over GF(2) with n=520, k=12 and d=236.
This code was found by Heurico 1.16 in 0.672 seconds.