The generator matrix

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

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+103x^52+202x^53+253x^54+284x^55+219x^56+190x^57+180x^58+156x^59+117x^60+122x^61+67x^62+28x^63+56x^64+20x^65+14x^66+12x^67+8x^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 1.16 in 0.212 seconds.