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 2X+2  1  1  1  1  1  1  1  1  1 2X  1  1  1  1
 0  2  0  2  0  2  0  2  0  2 2X 2X+2  0  2 2X+2  0 2X  2 2X+2  0 2X  2 2X+2  0 2X  2 2X 2X+2  2  0 2X+2  0 2X  2 2X  2  0 2X+2 2X+2 2X 2X 2X 2X  2 2X+2 2X+2  0 2X  0  0 2X  2  0 2X 2X+2  2 2X+2 2X+2 2X+2 2X+2 2X  2 2X+2  0  0
 0  0 2X  0  0  0  0  0  0  0  0  0  0  0  0  0 2X  0  0 2X 2X 2X 2X 2X 2X  0  0 2X 2X  0  0 2X 2X  0 2X 2X  0 2X 2X 2X 2X  0 2X 2X  0 2X 2X  0 2X 2X  0 2X  0  0 2X  0 2X 2X 2X  0  0 2X 2X  0  0
 0  0  0 2X  0  0  0 2X  0  0  0  0 2X 2X 2X 2X  0  0 2X 2X 2X 2X  0 2X 2X  0 2X 2X  0 2X 2X 2X  0  0  0 2X 2X  0 2X  0  0  0  0 2X  0  0  0  0 2X 2X  0  0 2X 2X  0 2X  0  0 2X 2X  0 2X 2X  0 2X
 0  0  0  0 2X  0  0  0  0  0  0  0  0  0  0  0 2X 2X 2X 2X  0 2X 2X  0  0 2X 2X 2X 2X 2X 2X 2X  0 2X 2X  0 2X 2X  0  0  0 2X 2X 2X 2X  0 2X 2X 2X  0  0  0 2X  0  0 2X 2X  0  0 2X  0 2X  0 2X 2X
 0  0  0  0  0 2X  0 2X 2X  0 2X 2X 2X 2X  0 2X  0 2X  0 2X 2X  0 2X  0  0  0 2X 2X  0 2X 2X  0 2X 2X 2X  0  0  0 2X  0 2X  0 2X  0  0  0  0 2X  0 2X  0 2X  0  0  0 2X 2X 2X 2X  0  0 2X  0 2X 2X
 0  0  0  0  0  0 2X  0 2X 2X  0 2X  0 2X 2X 2X 2X  0  0 2X 2X 2X 2X 2X  0 2X  0  0  0 2X 2X 2X 2X 2X  0 2X  0 2X 2X  0  0 2X 2X  0  0 2X  0 2X  0  0  0 2X 2X  0  0  0  0  0  0 2X  0 2X  0  0  0

generates a code of length 65 over Z4[X]/(X^2+2X+2) 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 code over GF(2) with n=520, k=11 and d=240.
This code was found by Heurico 1.16 in 0.36 seconds.