The generator matrix

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

generates a code of length 57 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+115x^52+200x^53+214x^54+288x^55+258x^56+202x^57+182x^58+144x^59+97x^60+80x^61+83x^62+68x^63+32x^64+30x^65+32x^66+12x^67+5x^68+1x^70+3x^72+1x^76

The gray image is a code over GF(2) with n=228, k=11 and d=104.
This code was found by Heurico 1.16 in 0.214 seconds.