The generator matrix

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

generates a code of length 57 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+218x^53+537x^54+640x^55+494x^56+524x^57+528x^58+476x^59+295x^60+178x^61+97x^62+60x^63+25x^64+16x^65+4x^66+1x^68+2x^78

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 0.296 seconds.