The generator matrix

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

generates a code of length 65 over Z2[X]/(X^4) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+168x^60+192x^61+534x^62+368x^63+575x^64+416x^65+692x^66+384x^67+384x^68+160x^69+142x^70+16x^71+49x^72+8x^74+3x^76+2x^80+1x^88+1x^92

The gray image is a linear code over GF(2) with n=520, k=12 and d=240.
This code was found by Heurico 1.16 in 1.25 seconds.