The generator matrix

 1  0  1  1  1 X+2  1  1  X  1  1  2  1  1  2  X  1  1  1  1 X+2  0  1  1  0  2  2  X  X  2  2 X+2  1  X  X  1  1  1  1  X  1  2  1  1  1  0  X  2  0  1  1  1  X  1  1  1  1  X
 0  1  1 X+2 X+3  1  2 X+1  1  X  3  1  0  1  1  1  2  3  X X+1  1  1  2  1  1  1  1  1  1  1  1  1 X+1  1  1  X X+3 X+3  2  1 X+3  1  3 X+3 X+2  X  1  1  1  0 X+3  X  1 X+3 X+1 X+1  2  0
 0  0  X  0 X+2  0  X  2  X  X  2 X+2  0  X X+2 X+2 X+2  2 X+2  2  2  0  0 X+2  0  0  X X+2  0  2  X X+2  X X+2  0  X X+2 X+2 X+2  0  X X+2  X  2  2 X+2  2  X  X  X  0  0 X+2 X+2 X+2  X X+2  0
 0  0  0  2  0  0  0  2  2  0  0  0  0  0  0  2  0  0  2  0  2  2  0  2  0  2  2  0  0  2  2  0  2  2  2  2  0  2  2  0  0  0  2  0  2  0  2  0  0  2  2  0  2  0  2  0  2  0
 0  0  0  0  2  0  0  0  0  2  0  2  0  2  2  0  2  0  2  2  2  2  2  2  2  0  2  0  2  2  0  0  0  2  0  2  0  2  0  2  2  0  0  0  2  0  2  2  0  2  2  0  2  2  0  2  2  2
 0  0  0  0  0  2  2  2  0  0  0  0  2  2  2  2  2  2  2  2  0  2  0  0  2  0  0  2  0  0  2  0  0  2  2  0  2  0  0  2  2  0  2  2  2  2  2  2  0  0  2  2  0  2  2  0  0  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+64x^52+116x^53+197x^54+220x^55+198x^56+192x^57+180x^58+184x^59+158x^60+180x^61+129x^62+108x^63+48x^64+24x^65+27x^66+8x^68+8x^70+1x^72+1x^74+1x^76+2x^78+1x^84

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 0.283 seconds.