The generator matrix

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

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+80x^55+282x^56+312x^57+760x^58+654x^59+1394x^60+948x^61+1793x^62+1122x^63+1845x^64+1124x^65+1856x^66+920x^67+1310x^68+576x^69+626x^70+254x^71+256x^72+96x^73+80x^74+32x^75+24x^76+12x^77+5x^78+8x^79+8x^80+4x^81+2x^83

The gray image is a code over GF(2) with n=256, k=14 and d=110.
This code was found by Heurico 1.16 in 12.2 seconds.