The generator matrix

 1  0  1  1  1  0  1 X+2  1  1 X+2  1  1  2  1  1  1  2  X  1  X  1  1  1  X  1  X  1  1  0  1  1  X  0  1  1  1  2  1  0  2  1  2  1  1  1  1  1  1  X  X X+2  1  0 X+2  X  1  1
 0  1  1  0 X+3  1  X  1 X+3  X  1  1  2  1 X+1  0 X+3  1  1 X+2  1  3  X X+3  1  1  1  1 X+3  1 X+3  2  1  1  3  0 X+2  1 X+1  2  1  0  2  1  1  1  3  X X+2  X  1  1  0  1  1  0  3  0
 0  0  X  0 X+2  X  0  X  0  X  2  0  X  0  2 X+2  X  X X+2  2  0 X+2  X  2  0  2 X+2  X  2  2  0  2  X  X  0  2  0  2  2  X  X X+2  X  0  2  X  X  0  0  X  X  X  2 X+2 X+2  0  X  0
 0  0  0  X  0  X  X  X X+2  0  2 X+2  2  X  2  X X+2  2  2  0 X+2 X+2 X+2 X+2  2  2  0  X X+2 X+2  0  X  2  X  X  2  2  0  0 X+2  0  X  X  0  2  2  2  X  X X+2 X+2  X X+2  2  2  X X+2  0
 0  0  0  0  2  2  2  0  2  2  2  0  0  0  0  0  0  0  2  2  2  0  2  2  0  0  2  2  0  2  2  2  0  0  2  2  0  2  0  2  2  2  2  2  2  2  0  0  2  0  2  2  0  0  0  2  0  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+57x^52+130x^53+201x^54+228x^55+209x^56+190x^57+163x^58+196x^59+177x^60+138x^61+119x^62+80x^63+46x^64+36x^65+22x^66+20x^67+19x^68+2x^70+4x^71+2x^72+2x^73+5x^74+1x^76

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 0.279 seconds.