The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+80x^52+312x^53+284x^54+480x^55+604x^56+592x^57+584x^58+480x^59+295x^60+312x^61+60x^62+4x^64+5x^68+2x^72+1x^88

The gray image is a code over GF(2) with n=456, k=12 and d=208.
This code was found by Heurico 1.16 in 0.281 seconds.