The generator matrix

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

generates a code of length 65 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 65.

Homogenous weight enumerator: w(x)=1x^0+34x^65+17x^66+2x^67+4x^68+2x^69+1x^70+2x^71+1x^72

The gray image is a code over GF(2) with n=520, k=6 and d=260.
This code was found by Heurico 1.16 in 0.187 seconds.