The generator matrix

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

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+408x^53+1048x^54+1130x^55+1471x^56+1016x^57+1034x^58+604x^59+570x^60+352x^61+290x^62+170x^63+62x^64+32x^65+2x^66+2x^70

The gray image is a code over GF(2) with n=456, k=13 and d=212.
This code was found by Heurico 1.16 in 13.8 seconds.