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

generates a code of length 64 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+64x^57+110x^58+134x^59+56x^60+228x^61+101x^62+358x^63+31x^64+364x^65+83x^66+208x^67+26x^68+92x^69+59x^70+56x^71+7x^72+20x^73+23x^74+10x^75+2x^76+8x^78+2x^79+4x^80+1x^104

The gray image is a code over GF(2) with n=256, k=11 and d=114.
This code was found by Heurico 1.16 in 13.2 seconds.