The generator matrix

 1  0  0  1  1  1  X  1  1 X+2  1  1  X X+2  X  0  1  1  1  1 X+2 X+2  1  2  0  1  1  1 X+2  1  1  0 X+2  1  1  2  1  0  2  2  1  1 X+2  0  1  0  1  0  1  1  1  1  1  2  1  1  1  1  0  1  1 X+2 X+2  1
 0  1  0  X  1 X+3  1 X+2  0  2  1 X+1 X+2  1  1  1 X+2 X+3  0  3  1  1  X  1 X+2  1 X+2  1  1  0 X+1  1 X+2  0  3  1  1  1  1  2 X+3  X  X  1 X+1  1  X  1  0  3  1  0 X+2  1  X X+3 X+2 X+2  1 X+3  1  1  1  0
 0  0  1  1 X+3 X+2  1 X+1 X+2  1  1  0  1 X+1  X X+1  2  1 X+3 X+2  0  X  X  3  1  0  3 X+1 X+1 X+1  1  2  1  X  2 X+2  1 X+1  0  1  3  2  1  3  X  0 X+3 X+3  X  3 X+3  0  2 X+3 X+3  1  2  X  0  X  2  X X+3  0
 0  0  0  2  0  0  0  0  2  2  0  0  0  2  2  2  2  0  0  2  2  0  0  0  2  2  2  0  0  0  0  2  2  2  0  2  0  0  0  0  0  2  2  0  0  2  0  2  0  2  0  2  2  0  2  2  2  0  2  2  2  0  2  0
 0  0  0  0  2  0  0  0  0  0  0  2  2  2  2  2  0  2  2  0  0  2  2  2  0  0  2  0  2  2  2  2  0  2  2  0  2  2  0  0  0  2  0  0  0  0  0  0  0  0  2  2  0  0  0  2  2  2  2  0  0  0  2  2
 0  0  0  0  0  2  0  0  0  0  0  2  0  0  0  0  0  0  0  2  0  0  2  2  2  0  2  2  2  2  2  2  2  2  0  2  2  0  0  2  0  2  0  2  0  2  2  2  0  0  2  0  2  2  0  2  0  0  0  0  2  0  2  2
 0  0  0  0  0  0  2  0  0  0  0  0  0  2  0  0  2  2  2  2  2  2  0  2  2  0  2  2  0  2  2  0  0  0  2  0  0  0  2  0  2  2  2  0  0  2  2  0  2  0  2  0  0  2  2  0  2  2  2  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+38x^56+276x^57+271x^58+586x^59+419x^60+836x^61+593x^62+902x^63+539x^64+946x^65+557x^66+748x^67+328x^68+526x^69+198x^70+176x^71+68x^72+90x^73+33x^74+18x^75+13x^76+14x^77+9x^78+2x^79+2x^80+3x^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 2.96 seconds.