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.