The generator matrix

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

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+99x^52+206x^53+257x^54+264x^55+227x^56+214x^57+176x^58+164x^59+109x^60+94x^61+63x^62+40x^63+64x^64+20x^65+18x^66+12x^67+4x^68+8x^69+6x^70+2x^73

The gray image is a code over GF(2) with n=228, k=11 and d=104.
This code was found by Heurico 1.11 in 0.131 seconds.