The generator matrix

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

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+668x^54+552x^55+951x^56+528x^57+388x^58+248x^59+328x^60+128x^61+200x^62+16x^63+84x^64+2x^68+2x^72

The gray image is a code over GF(2) with n=456, k=12 and d=216.
This code was found by Heurico 1.16 in 69.5 seconds.