The generator matrix

 1  0  1  1  1  X  1  1 X^2+X+2  1  1 X^2+X X^2+X+2 X^2  1  1  1  1 X^2+X+2  1  1 X^2+2  1  X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  X  1 X^2+2 X+2  1 X^2+2  1  0  1  1 X^2+2
 0  1  1 X^2 X+1  1  X  3  1 X+2 X^2+X+1  1  1  1 X^2 X^2+3 X+2 X+1  1  2 X^2+X+3  1  X  1  3 X+1 X^2  1 X^2+X X^2+X X^2+3  2 X^2+X+3 X^2+X+2 X^2+1  2 X^2+X+3 X^2+2 X+3 X^2+X X^2+X+2 X^2+3 X^2+1 X^2+2  X  1  1 X^2+X  1  1 X^2+1  1 X^2+X+3  1 X+1 X+3  X
 0  0  X X+2  2 X+2 X+2  2 X^2+X+2  0  X  0 X^2+2 X^2 X^2+X+2 X^2+2 X^2+X+2 X^2  X X^2+2 X^2+X X^2+X X^2+2 X^2+X+2 X^2+X X^2+X+2 X^2 X^2 X^2+X X+2  2  X  0 X^2+2 X^2+X X^2+X X^2+2  2 X+2  0  2  X X+2  0 X^2+X X+2 X^2 X^2  0  2 X^2 X+2 X^2  X  X  X X+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+339x^54+320x^55+324x^56+180x^57+297x^58+220x^59+290x^60+44x^61+10x^62+4x^63+8x^64+8x^66+1x^70+1x^72+1x^82

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 0.125 seconds.