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  X  1  1  X  X  1  X  1  1  1  1  X  0  1  1  X  X  1  1  1  X  1  0  1  X  1  X  2  0  X  0  X  0
 0  X  0  0  0  X X+2  X  0  2  2  0  X X+2  X X+2 X+2 X+2 X+2  2  0  0 X+2  2 X+2  0  2  X  X  2  X  0  X X+2  2 X+2  0  X  0 X+2  2 X+2  X  0 X+2  2 X+2  X  0  X  X  2 X+2  X  2  X X+2  0  X  X  0  X X+2  2
 0  0  X  0  X  X X+2  0  0  0 X+2 X+2  X  X  2  0  X  2  0 X+2 X+2  2 X+2  2  0  2  X  2  X  X  X  0  2  0  X  2  2  X X+2 X+2 X+2  X  2  X X+2  0  2  0  0  X  2  X  X X+2  X  0  X  2 X+2 X+2  X  2  0  X
 0  0  0  X  X  0 X+2  X  2 X+2  X  2  2  X  X  2  0 X+2  0  X  2  X  X  0  0  X  2 X+2 X+2  X  X X+2 X+2 X+2  0  0  2  0  2  2  X  0  X  2  X  X  2  X  0  2  2  2  0  2  2  0  X  X  0  X  0  2  0  2
 0  0  0  0  2  0  0  0  2  0  0  0  0  0  0  2  2  2  2  2  0  2  2  0  2  0  2  2  2  0  0  0  0  0  2  0  2  0  0  2  2  0  0  0  2  2  2  0  2  2  2  2  2  0  2  0  2  0  0  2  2  2  2  2
 0  0  0  0  0  2  0  2  0  0  2  2  0  2  2  0  0  0  2  2  2  0  0  2  0  2  2  0  2  0  0  2  0  0  2  0  2  0  0  2  2  2  2  2  2  2  2  2  2  0  0  0  2  0  2  2  0  2  2  0  0  2  0  0
 0  0  0  0  0  0  2  2  2  2  0  0  2  0  0  0  0  0  2  0  2  0  2  2  2  2  2  2  0  0  0  0  0  2  2  2  2  0  2  0  2  2  2  0  2  2  0  0  0  0  2  2  2  0  0  0  2  2  0  2  0  2  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+186x^56+24x^57+306x^58+52x^59+403x^60+156x^61+440x^62+316x^63+518x^64+228x^65+442x^66+140x^67+314x^68+100x^69+198x^70+4x^71+134x^72+4x^73+76x^74+34x^76+10x^78+9x^80+1x^92

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 3.32 seconds.