The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+102x^53+476x^54+744x^55+825x^56+502x^57+405x^58+328x^59+268x^60+130x^61+168x^62+96x^63+25x^64+18x^65+6x^66+1x^72+1x^74

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 0.187 seconds.