The generator matrix

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

generates a code of length 65 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 61.

Homogenous weight enumerator: w(x)=1x^0+84x^61+590x^62+704x^63+692x^64+556x^65+509x^66+272x^67+233x^68+148x^69+122x^70+64x^71+73x^72+28x^73+18x^74+1x^82+1x^84

The gray image is a code over GF(2) with n=520, k=12 and d=244.
This code was found by Heurico 1.16 in 0.218 seconds.