The generator matrix

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

generates a code of length 64 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+120x^55+611x^56+986x^57+1341x^58+1692x^59+1898x^60+2412x^61+2788x^62+2954x^63+3188x^64+3152x^65+2662x^66+2426x^67+2091x^68+1594x^69+1174x^70+732x^71+472x^72+220x^73+129x^74+72x^75+25x^76+18x^77+2x^78+2x^79+2x^81+2x^83+2x^84

The gray image is a code over GF(2) with n=256, k=15 and d=110.
This code was found by Heurico 1.13 in 15.4 seconds.