The generator matrix

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

generates a code of length 64 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+166x^56+12x^57+284x^58+64x^59+430x^60+124x^61+456x^62+308x^63+526x^64+312x^65+474x^66+136x^67+282x^68+60x^69+194x^70+4x^71+133x^72+4x^73+84x^74+23x^76+10x^78+6x^80+2x^82+1x^100

The gray image is a code over GF(2) with n=256, k=12 and d=112.
This code was found by Heurico 1.16 in 1.37 seconds.