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  X  1  1  1  1  1  1  1  1  1 2X  1  1  1  1  X  1  2  1  X  1 2X  1  1  1  1  2  X 2X 2X+2  X  X  1  X  1
 0  X  0  X 2X  0 3X+2 3X+2  2  X 2X+2 3X X+2  2  2 3X+2  2 3X 2X 3X+2 2X 3X+2 2X X+2  0  X  0  X  2  X 2X+2  0 X+2  2 X+2 X+2 2X+2  X 2X  2  X  X 2X  0 3X+2  X  0  X 2X X+2 3X 2X+2  X X+2 X+2 X+2  X 3X  X  X 3X X+2  0 3X X+2
 0  0  X  X  0 3X+2 3X+2 2X  2 3X  X  2 3X+2 X+2 2X+2  2  X 3X+2 2X+2  0 2X+2 2X+2 3X 3X 3X 3X+2  0 2X+2 2X+2 2X 3X+2 X+2  X  2 2X  X  X 2X+2  X 2X X+2 X+2 3X+2 X+2 2X  0  2  2 2X+2 X+2  X  X 2X+2 2X+2  0 2X+2 2X+2 3X  X  0  0 2X+2  X  X 3X
 0  0  0  2  2 2X+2 2X 2X+2  0 2X  2  2  2 2X  2 2X  0 2X 2X+2 2X 2X 2X+2  2  2 2X+2  2 2X 2X+2 2X 2X 2X+2  0  0 2X+2  2 2X+2 2X+2 2X 2X 2X+2  2  0 2X  2  0 2X+2  2  0  0  0  0  0  0  0  2 2X+2 2X  2 2X+2 2X+2 2X 2X 2X+2 2X+2  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+233x^60+240x^61+340x^62+416x^63+529x^64+780x^65+414x^66+408x^67+312x^68+140x^69+108x^70+52x^71+73x^72+8x^73+34x^74+4x^75+3x^76+1x^104

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 2.42 seconds.