The generator matrix

 1  0  1  1  1 X+2  1  1  X  1  1  2  1  1 X+2  1  1  X  1  2  1  1  1  0  1  1  1  1  1  1  1  1  1  2  1  2  1  1  X  X  1  0  1  X  0  X  1  1  0  0  1  1  1  1 X+2 X+2  1  2  1  1  2  2  X  1
 0  1  1 X+2 X+3  1  2 X+1  1  X  3  1 X+2  1  1  0 X+1  1 X+3  1  2  X  3  1  2  X  0 X+2  X  X  X  X X+1  1 X+1  1  3  3  1  1 X+1  1  3  1  1  1  1 X+1  1  0  3  0 X+3  3  1  1 X+1  1  2 X+2  1  1  0  X
 0  0  X  0 X+2  0  X  2  X  X  2  X  0  X  0  2  0 X+2  X  X  X X+2  2  2  X  0 X+2  2  X X+2  2  0  0 X+2 X+2  2 X+2  0 X+2  2  2  X  2  X  2  0  X  X  0  X  2  2  X X+2  0 X+2 X+2  0 X+2 X+2  X  X  2 X+2
 0  0  0  2  0  0  0  2  2  0  2  2  2  0  0  0  0  0  2  2  2  2  2  2  2  2  0  0  2  0  0  2  0  0  0  2  2  0  0  2  0  0  2  2  0  0  2  2  0  2  2  0  0  2  2  2  2  0  0  0  0  2  0  2
 0  0  0  0  2  0  0  0  0  2  2  2  2  2  2  2  2  2  2  2  0  2  2  0  0  0  2  2  2  0  0  2  2  0  0  2  2  0  2  2  0  2  0  2  0  0  0  0  2  0  0  0  0  2  0  0  0  2  2  2  2  0  2  0
 0  0  0  0  0  2  2  2  0  0  0  2  2  2  0  2  2  0  0  0  2  0  2  0  0  2  2  0  2  0  2  0  0  0  2  2  2  2  2  0  0  0  0  0  2  0  2  0  2  2  2  2  0  0  2  2  2  0  0  2  2  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+97x^58+144x^59+160x^60+180x^61+203x^62+196x^63+178x^64+200x^65+157x^66+152x^67+114x^68+132x^69+71x^70+20x^71+18x^72+10x^74+4x^76+3x^80+4x^82+2x^84+2x^86

The gray image is a code over GF(2) with n=256, k=11 and d=116.
This code was found by Heurico 1.16 in 0.353 seconds.