The generator matrix

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

generates a code of length 57 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+716x^54+392x^55+1082x^56+420x^57+580x^58+200x^59+346x^60+36x^61+170x^62+40x^63+105x^64+6x^66+2x^72

The gray image is a code over GF(2) with n=456, k=12 and d=216.
This code was found by Heurico 1.16 in 21.1 seconds.