The generator matrix

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

generates a code of length 57 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+348x^54+256x^55+396x^56+152x^57+376x^58+216x^59+208x^60+8x^61+54x^62+8x^63+17x^64+4x^66+2x^70+1x^72+1x^88

The gray image is a code over GF(2) with n=456, k=11 and d=216.
This code was found by Heurico 1.16 in 77.7 seconds.