The generator matrix

 1  0  0  1  1  1  X  1 X+2  1  1  X  1 X+2  1  X  2  1  1  X  1  1  0  0  1  1  1  2  2  1  1 X+2  1 X+2  1  0  1 X+2  1  1  1 X+2  1  0  1  1  1  2  1  X  1  2  1  X  1 X+2  1  1  1  X  1  X  X  1
 0  1  0  0  1 X+3  1  2  0  2 X+3  1 X+1  1  1 X+2  1  X  X  1  X  3  X  1 X+1  1  2  1  1 X+3 X+3  1  X  0 X+3  1  2  1 X+1  3 X+2  1  1  1 X+1  3 X+1 X+2  2  1  2  1  X  1  X  1  3  0  3 X+2  X  1  0  0
 0  0  1  1 X+1  0  1 X+1  1  X X+1  X  X X+1  3  1  X X+2  0  2 X+1 X+2  1 X+1  0  1  1  1  0  2  3 X+3 X+1  1  X X+1  0 X+2 X+3  1 X+2 X+1  0  1  3  2 X+2  1  1  3  3  2  1  1 X+1 X+1  X X+1 X+1  1 X+3  X  2  0
 0  0  0  X  X X+2  2 X+2  0  0  X  2  X  0 X+2  0  0  2  2  2 X+2  X  0  2 X+2  0  0  X X+2  2  2  X  2 X+2  0 X+2  X X+2  0  0  X X+2  2  0  X  2 X+2  X X+2  X  X X+2  0  0  X  2  0 X+2  2  X  2  2  X  0
 0  0  0  0  2  0  0  2  2  2  0  2  2  0  0  2  0  0  2  2  0  0  0  2  2  2  0  2  0  2  0  2  2  2  0  0  2  0  0  2  0  0  0  2  2  2  2  2  2  2  2  2  2  0  2  2  2  0  0  2  2  0  0  0
 0  0  0  0  0  2  2  0  0  0  0  0  0  0  2  2  2  2  2  2  2  0  2  0  2  2  2  0  2  0  0  2  0  2  0  2  2  0  2  0  0  2  2  0  2  2  0  0  2  2  0  0  0  0  2  2  2  2  0  2  2  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+88x^56+168x^57+394x^58+468x^59+685x^60+626x^61+823x^62+558x^63+826x^64+618x^65+703x^66+574x^67+551x^68+328x^69+321x^70+164x^71+135x^72+42x^73+55x^74+26x^75+16x^76+10x^77+4x^78+2x^79+2x^80+4x^82

The gray image is a code over GF(2) with n=256, k=13 and d=112.
This code was found by Heurico 1.16 in 3.14 seconds.