The generator matrix

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

generates a code of length 64 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 59.

Homogenous weight enumerator: w(x)=1x^0+176x^59+341x^60+248x^61+586x^62+392x^63+795x^64+272x^65+528x^66+288x^67+240x^68+120x^69+36x^70+40x^71+18x^72+10x^76+2x^78+2x^88+1x^92

The gray image is a code over GF(2) with n=512, k=12 and d=236.
This code was found by Heurico 1.16 in 78.1 seconds.