The generator matrix

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

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+22x^56+132x^57+159x^58+246x^59+298x^60+334x^61+386x^62+358x^63+387x^64+330x^65+359x^66+292x^67+266x^68+192x^69+93x^70+112x^71+34x^72+24x^73+17x^74+14x^75+10x^76+10x^77+8x^78+2x^79+4x^80+2x^81+1x^82+2x^84+1x^86

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 0.964 seconds.