The generator matrix

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

generates a code of length 64 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 61.

Homogenous weight enumerator: w(x)=1x^0+332x^61+374x^62+314x^63+199x^64+232x^65+252x^66+220x^67+39x^68+36x^69+29x^70+10x^71+8x^77+1x^84+1x^86

The gray image is a code over GF(2) with n=512, k=11 and d=244.
This code was found by Heurico 1.16 in 0.531 seconds.