The generator matrix

 1  0  0  0  1  1  1  2  0  1  1  1  0  1  0  2  1  X X+2  1  X X+2  1  1  1  1  2  1  1  1  1  2  X  0  1  0  X  2  X  1 X+2  1  0  1  0 X+2  1 X+2  1  1  1  0 X+2  1  X  1  2
 0  1  0  0  0  1  1  1  2  0  2  1  1  3  1  1  X  X  1  3  1  1  0 X+3 X+1  2  X  0  2  3 X+1  1  1  1 X+3  X  1  1 X+2 X+3  X X+3  0 X+2  1  2 X+1 X+2  1 X+2  0  1  0 X+1  X  3  1
 0  0  1  0  1  2  3  1  1  2  1  1  2  2  3 X+1 X+3  1  X  0  X  1 X+3 X+1 X+3  X  0 X+2  3  2  0 X+3  2  X  1  1  0  X  1 X+3  X X+2  1  X  2  1  3  1 X+3 X+1  X  0  X  2  0 X+2 X+1
 0  0  0  1  2  0  2  2  1  1  3  1  3  3  1  X X+2 X+2 X+2 X+2 X+3 X+1 X+3 X+1  0  0  1  3 X+3 X+1  2  2  X  X X+3 X+1 X+1  0  0  1  1 X+2 X+2  X X+1 X+1  1  2 X+1  0 X+1  X  1  2  1  0 X+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+558x^52+844x^54+860x^56+668x^58+558x^60+312x^62+201x^64+60x^66+28x^68+4x^70+2x^72

The gray image is a code over GF(2) with n=228, k=12 and d=104.
This code was found by Heurico 1.11 in 61 seconds.