The generator matrix

 1  0  1  1  1 X+2  1  1  0  1  1 X+2  1  1 X+2  1  1  0  1  0  1  1 X+2  1  1  1  0  1  1  1  2  1 X+2  1  1  1  1  1  1  1 X+2  1  0  X  1  1  1  1  X  1  1  1  1 X+2 X+2 X+2  1  1  1  1  1  1  X  2
 0  1 X+1 X+2  1  1  0 X+1  1 X+2  3  1  0 X+1  1 X+2  3  1  3  1 X+2 X+1  1  0  0 X+1  1 X+2  3  1  1  0  1  X X+3  3  2 X+2  3  0  1 X+1  1  1  3  2 X+1 X+3  1 X+3  2 X+2  3  1  1  1 X+1  2  X  3 X+1 X+1  2  0
 0  0  2  0  0  0  0  0  0  0  0  2  0  2  2  2  2  2  0  2  2  0  2  2  0  2  0  2  0  2  2  0  0  0  2  0  2  2  0  0  0  0  2  0  2  2  0  2  2  2  0  2  2  2  0  2  2  2  0  2  0  0  0  2
 0  0  0  2  0  0  0  0  0  2  0  2  2  0  2  0  2  0  2  0  2  2  2  2  2  2  0  2  0  2  0  2  2  2  0  2  2  0  0  0  0  0  2  0  0  0  0  2  0  0  2  2  0  0  2  0  2  0  2  2  0  0  2  2
 0  0  0  0  2  0  0  0  0  2  2  0  2  2  0  0  2  2  2  2  0  0  2  2  2  2  2  0  2  2  0  0  2  2  2  0  0  2  2  0  0  2  0  0  0  0  2  0  0  2  0  0  0  0  2  0  0  0  2  0  2  0  2  0
 0  0  0  0  0  2  0  0  2  0  2  2  0  0  2  2  2  0  0  2  2  2  0  2  0  0  0  0  2  2  0  0  2  2  2  2  2  0  0  2  0  2  0  0  2  2  0  0  0  2  2  0  0  2  2  0  0  0  0  2  2  0  2  2
 0  0  0  0  0  0  2  0  2  0  0  0  2  0  2  0  2  2  2  2  2  2  2  0  0  0  0  2  2  0  2  2  2  0  2  0  0  2  2  2  2  0  2  0  0  2  2  0  0  0  0  2  2  0  0  0  0  2  2  2  0  2  0  0
 0  0  0  0  0  0  0  2  2  0  2  0  0  2  2  2  2  0  2  0  2  0  2  2  2  0  2  0  0  0  2  2  2  2  2  2  0  0  0  0  0  0  0  2  2  0  2  2  0  2  2  2  2  0  0  2  0  2  2  2  2  2  2  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+93x^56+40x^57+216x^58+100x^59+502x^60+164x^61+474x^62+212x^63+550x^64+196x^65+522x^66+172x^67+383x^68+108x^69+190x^70+28x^71+108x^72+4x^73+6x^74+14x^76+5x^80+5x^84+3x^88

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 0.994 seconds.