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

generates a code of length 58 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+55x^52+83x^54+231x^56+363x^58+178x^60+37x^62+20x^64+25x^66+26x^68+4x^70+1x^108

The gray image is a code over GF(2) with n=232, k=10 and d=104.
This code was found by Heurico 1.16 in 0.178 seconds.