The generator matrix

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

generates a code of length 64 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+80x^57+145x^58+316x^59+257x^60+456x^61+272x^62+470x^63+276x^64+436x^65+244x^66+452x^67+181x^68+230x^69+81x^70+74x^71+35x^72+18x^73+20x^74+12x^75+15x^76+10x^77+4x^78+4x^79+2x^80+2x^81+1x^82+1x^84+1x^86

The gray image is a code over GF(2) with n=256, k=12 and d=114.
This code was found by Heurico 1.16 in 1.04 seconds.