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  2  1  1  X  1  1  1  1  1  1  1  X  1  1  1  1  1  1  0  1  1  1  1  0  1  2
 0  X  0  0  0  2  0  2  0 X+2  X X+2 X+2  X X+2  X  2 X+2  0  X  0  X  2 X+2  0  X  2  0  2  X  X  X  X  0  0  X  2  2  X  X  0  2  2  X  0 X+2 X+2  0 X+2  2  X  0  X X+2  0  0 X+2  2
 0  0  X  0  0  2 X+2  X X+2  X  X  X X+2  0  0  0  2  2  2  X X+2  2  X  X  0  0 X+2  2  X  X  0 X+2  X  2  0 X+2  X  2  2 X+2  X  0  2  0  X X+2 X+2  X  0  X  X  2 X+2  X  2  X  2  0
 0  0  0  X  0  X X+2  X  2  0 X+2  X  0  X  X  2  0  0  X  X  2 X+2 X+2  0  0 X+2 X+2 X+2  0 X+2  0  2  2  2 X+2 X+2 X+2  2  2  X X+2 X+2  2  X  2  0  0  0  2  2  2  0  0 X+2  0  X  0  X
 0  0  0  0  X  X  2 X+2  X  X X+2  0  0  2 X+2 X+2 X+2  0  2 X+2 X+2 X+2  0  0  2  0  X X+2  2  2  X X+2  0  2  X X+2  X  2 X+2  X  X  2 X+2  0  2  2  X  X  X  X  X X+2  0 X+2  X  X  X 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+261x^52+36x^54+529x^56+472x^58+474x^60+36x^62+173x^64+65x^68+1x^104

The gray image is a code over GF(2) with n=232, k=11 and d=104.
This code was found by Heurico 1.16 in 0.392 seconds.