The generator matrix

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

generates a code of length 64 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+399x^60+368x^61+648x^62+432x^63+620x^64+416x^65+490x^66+240x^67+307x^68+80x^69+44x^70+36x^72+2x^74+9x^76+3x^80+1x^84

The gray image is a code over GF(2) with n=512, k=12 and d=240.
This code was found by Heurico 1.16 in 2.23 seconds.