The generator matrix

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

generates a code of length 65 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+61x^60+312x^61+454x^62+528x^63+531x^64+488x^65+514x^66+404x^67+423x^68+232x^69+34x^70+56x^71+18x^72+24x^73+2x^74+4x^75+2x^76+1x^80+4x^82+2x^84+1x^88

The gray image is a code over GF(2) with n=520, k=12 and d=240.
This code was found by Heurico 1.16 in 0.375 seconds.