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  X  1  1  1  1  1  1  1  1  1  1 X^2  1  1  1  1  1  1  1  1  1 X^3  1  1  1  1
 0 X^3+X^2  0 X^3+X^2  0 X^3+X^2  0 X^3+X^2  0 X^3+X^2 X^3 X^2  0 X^3+X^2 X^2  0 X^3 X^3+X^2 X^2  0 X^3 X^3+X^2 X^2  0 X^3 X^3+X^2 X^3 X^2 X^3+X^2  0 X^2  0 X^3 X^3+X^2 X^3 X^3+X^2  0 X^2 X^2 X^3 X^3 X^3 X^3 X^3+X^2 X^2 X^2  0 X^3  0  0 X^3 X^3+X^2  0 X^3 X^2 X^3+X^2 X^2 X^2 X^2 X^2 X^3 X^3+X^2 X^2  0  0
 0  0 X^3  0  0  0  0  0  0  0  0  0  0  0  0  0 X^3  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0  0 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0 X^3  0  0 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3  0  0
 0  0  0 X^3  0  0  0 X^3  0  0  0  0 X^3 X^3 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3 X^3  0  0  0 X^3 X^3  0 X^3  0  0  0  0 X^3  0  0  0  0 X^3 X^3  0  0 X^3 X^3  0 X^3  0  0 X^3 X^3  0 X^3 X^3  0 X^3
 0  0  0  0 X^3  0  0  0  0  0  0  0  0  0  0  0 X^3 X^3 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3  0 X^3 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  0  0 X^3 X^3  0  0 X^3  0 X^3  0 X^3 X^3
 0  0  0  0  0 X^3  0 X^3 X^3  0 X^3 X^3 X^3 X^3  0 X^3  0 X^3  0 X^3 X^3  0 X^3  0  0  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3 X^3  0  0  0 X^3  0 X^3  0 X^3  0  0  0  0 X^3  0 X^3  0 X^3  0  0  0 X^3 X^3 X^3 X^3  0  0 X^3  0 X^3 X^3
 0  0  0  0  0  0 X^3  0 X^3 X^3  0 X^3  0 X^3 X^3 X^3 X^3  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3  0  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3  0 X^3 X^3  0  0 X^3 X^3  0  0 X^3  0 X^3  0  0  0 X^3 X^3  0  0  0  0  0  0 X^3  0 X^3  0  0  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+79x^60+128x^62+615x^64+512x^65+616x^66+16x^68+16x^70+8x^72+8x^74+48x^76+1x^124

The gray image is a linear code over GF(2) with n=520, k=11 and d=240.
This code was found by Heurico 1.16 in 0.375 seconds.