The generator matrix

 1  0  1  1  1  0  1 X+2  1  1 X+2  1  1  2  1  1  0  1  1  X  1  1  1 X+2  1 X+2  1  1  1  1  X  1  1  1  0  1  2  1  2  1 X+2 X+2  2  1 X+2  1  1  1  1  1  1  2  X  1  1  1  1
 0  1  1  0 X+3  1  X  1 X+3  X  1  1  2  1 X+1 X+2  1 X+1  0  1  X X+1  1  1  1  1  3 X+1  X  1  1  3  1  1  1 X+3  1 X+1  1  0  1  1  1  X  1  2  2  0 X+1  0 X+1  X  1  0 X+1 X+2  2
 0  0  X  0 X+2  X  0  X  0  X  0  2 X+2  X  X  X  0  2  X X+2  2  2 X+2  2  0 X+2  2  2  0 X+2  X  0 X+2  2  0  2  0 X+2  X  0  0 X+2  X X+2 X+2  0 X+2  0  X  2  2  X  X X+2  X  0  2
 0  0  0  X  0  X  X  X X+2  0  2  X  2  2 X+2  X  X  0 X+2  2  0 X+2  0 X+2  2  X  2  X X+2  2  2  0 X+2  X  2  0 X+2 X+2  0  2  X  X X+2  0  2  X X+2 X+2  X  0  2  X  0 X+2  2  0  2
 0  0  0  0  2  2  2  0  2  2  2  0  0  2  2  2  0  0  0  0  2  2  0  2  0  0  2  0  0  2  0  2  2  2  2  2  2  0  0  2  0  2  0  0  2  2  0  2  2  0  0  0  2  2  0  0  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+300x^52+329x^54+482x^56+305x^58+385x^60+163x^62+52x^64+3x^66+19x^68+5x^72+4x^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 0.737 seconds.