The generator matrix

 1  0  1  1  1 X+2  1  1  0  1  1 X+2  1  1  0  1  1 X+2  1  1  0  1  1  1  2  1 X+2  1 X+2  1  1  X  1  1  1  1  1  1  1  1  1  1  1  0  X  1  X X+2 X+2  0 X+2  1  2  X  2  1  1  0
 0  1 X+1 X+2  1  1  0 X+1  1  3 X+2  1 X+1  0  1 X+2  3  1  0  3  1 X+2  2  3  1 X+1  1 X+1  1  0 X+3  1  X  0  2 X+2  X  2  3  3  X  3 X+2  1  2  1  1  1  1  1  1 X+1  1  1  1  0  2  X
 0  0  2  0  0  0  0  0  0  2  0  0  0  2  0  2  2  2  2  2  2  0  2  0  2  2  0  2  2  0  2  2  2  0  2  0  2  2  2  0  0  0  0  2  2  0  0  0  0  0  0  2  0  2  0  2  0  0
 0  0  0  2  0  0  0  2  0  0  2  0  0  2  2  2  0  0  2  0  0  2  2  0  2  0  0  2  0  2  2  0  2  0  0  2  2  0  0  0  2  2  0  2  2  2  0  2  2  0  2  0  0  2  0  2  2  2
 0  0  0  0  2  0  0  0  0  2  2  2  2  0  2  2  2  0  2  2  0  2  2  2  2  0  0  0  2  2  2  2  0  0  0  0  0  2  0  0  2  0  2  0  0  0  2  2  2  2  2  2  2  2  0  2  2  2
 0  0  0  0  0  2  0  2  0  0  0  2  0  2  2  2  2  2  0  2  2  2  0  2  0  0  2  0  0  2  2  2  2  2  0  2  2  0  2  0  0  2  2  0  0  2  0  2  0  2  2  0  2  0  2  2  2  2
 0  0  0  0  0  0  2  2  2  0  2  2  2  2  0  2  2  2  2  0  0  2  0  2  2  2  2  2  2  0  2  0  0  2  0  2  2  2  2  2  0  0  2  2  2  2  2  2  2  2  0  0  0  0  0  0  2  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+141x^52+40x^53+242x^54+104x^55+257x^56+112x^57+262x^58+112x^59+320x^60+104x^61+174x^62+40x^63+89x^64+26x^66+15x^68+3x^72+4x^76+2x^80

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 0.275 seconds.