The generator matrix

 1  0  0  0  1  1  1  2  0  1  1  1  1  0  X  X  1  1  2  1  X  X  1  1  0  X X+2  2  1 X+2  1  1 X+2  1  X  0  1  2  X  1  1 X+2  0  1  X  X  1  0  1  2  1  X  X  1  1  1  1  1
 0  1  0  0  0  2  2  2  1  3  1 X+1  3  1  1 X+2 X+2  2  1 X+3  1  X  X X+3  1  1  1  X X+1  0  0 X+2  1 X+1 X+2 X+2  3  1  1  1 X+3  1  0  3  0  1 X+2  1 X+2  1 X+3  1  1  2  3 X+1  1  2
 0  0  1  0  2  1  3  1 X+1  3  0  1 X+2  3  X  1 X+1  X  X X+2  1 X+2  0 X+3 X+3  2  3  1  X  1  1  X  2 X+2  1  2  0 X+3  2  1  1  1 X+2  0  0 X+1 X+2  0  X X+2  2  0 X+2  3 X+3  2 X+3  0
 0  0  0  1 X+3 X+3  0 X+1  2  X X+2  1  1 X+3 X+3 X+2 X+1 X+2  2 X+1  1  1  3  3  X  3 X+1 X+1  X  3  X  2  2  0  2  1 X+3  3 X+3  2 X+2 X+2  1  3  1  2 X+3  3  1  2  X  X  1  2  2  0 X+1  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+93x^52+318x^53+378x^54+454x^55+400x^56+380x^57+347x^58+400x^59+248x^60+304x^61+250x^62+184x^63+127x^64+86x^65+51x^66+32x^67+19x^68+14x^69+6x^70+2x^71+2x^73

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 0.581 seconds.