The generator matrix

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

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+111x^52+272x^53+383x^54+478x^55+393x^56+400x^57+411x^58+302x^59+304x^60+248x^61+224x^62+200x^63+148x^64+112x^65+47x^66+22x^67+19x^68+8x^69+7x^70+6x^71

The gray image is a code over GF(2) with n=232, k=12 and d=104.
This code was found by Heurico 1.11 in 0.301 seconds.