The generator matrix

 1  0  0  1  1  1 X+2  X  1  1  1  2  1  X  0  1  1  0  1  X  1  2  1  2  X  1  0  X  1  1  1  1 X+2  1  1  X  1  1  X  0 X+2  X X+2  1  1  1  1  1  1  1  1  X  1  0  1  1  X  1  1  2  1  1  1  0
 0  1  0  0  1 X+1  1  0  0  2 X+1  1  1  1  2  2  3  1  2  1  3  1  0  X  1 X+2 X+2  1  3  X X+1  1  1 X+2  2  1  1  1  X  1  1  X  0  3 X+3  X  X X+1 X+2  3  0  2  3  1 X+3 X+2  2 X+1 X+1  0  X  X X+1  X
 0  0  1  1  1  2  3  1 X+3  X  1 X+1  X X+2  1 X+2  X  X X+1 X+3  1  3  3  1  2  X  1 X+1 X+2  2  1  1  0  3 X+2  2  0  0  1  0 X+1  1  1 X+1 X+3  X X+3  2 X+1  2  0  1  3  0  1  3  1 X+2 X+1  1  2 X+1  X X+2
 0  0  0  X X+2  0 X+2 X+2 X+2  2 X+2  X  0  0 X+2 X+2  X X+2  0  2  0  2  2  2  X X+2 X+2 X+2  X  2  X  2  2  0  2  X  2 X+2 X+2  X X+2  0  0  2  2 X+2 X+2  X X+2 X+2  0 X+2  X  0  0  2  0  0  2  X  0  0  X X+2
 0  0  0  0  2  0  2  2  2  2  0  0  2  2  0  2  2  2  2  2  2  0  0  2  0  0  2  0  0  2  2  0  0  2  0  2  2  0  2  0  2  0  2  0  2  2  0  2  2  2  2  0  0  2  2  2  0  0  0  2  0  2  0  2

generates a code of length 64 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+168x^58+200x^59+495x^60+324x^61+548x^62+332x^63+449x^64+272x^65+310x^66+172x^67+256x^68+124x^69+178x^70+60x^71+96x^72+48x^73+38x^74+4x^75+13x^76+4x^78+2x^80+2x^86

The gray image is a code over GF(2) with n=256, k=12 and d=116.
This code was found by Heurico 1.16 in 0.876 seconds.