The generator matrix

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

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+363x^52+464x^54+993x^56+608x^58+858x^60+464x^62+267x^64+55x^68+17x^72+4x^76+2x^80

The gray image is a code over GF(2) with n=232, k=12 and d=104.
This code was found by Heurico 1.16 in 17.6 seconds.