The generator matrix

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

generates a code of length 57 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+202x^53+522x^54+518x^55+715x^56+546x^57+516x^58+354x^59+373x^60+180x^61+70x^62+20x^63+28x^64+32x^65+12x^66+4x^67+2x^72+1x^76

The gray image is a code over GF(2) with n=456, k=12 and d=212.
This code was found by Heurico 1.16 in 0.313 seconds.