The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+24x^54+296x^55+102x^56+176x^57+102x^58+296x^59+24x^60+1x^64+2x^82

The gray image is a code over GF(2) with n=456, k=10 and d=216.
This code was found by Heurico 1.16 in 0.109 seconds.