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

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+90x^60+554x^61+750x^62+698x^63+540x^64+478x^65+282x^66+262x^67+127x^68+104x^69+101x^70+72x^71+25x^72+8x^73+2x^74+1x^76+1x^78

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 0.219 seconds.