The generator matrix

 1  0  0  1  1  1  2  1  1  1  1  0  2 X^2  1  1 X^2+X+2  X  1  1  1 X^2+X+2  0  1  X X^2+X+2  1  1  1  1 X^2+2  1  1  1  1  1  1 X^2+X+2 X^2+2  1  1 X^2 X^2+X+2 X^2+X X^2+2  1  1  1  X  1  0  1  1  1  1  1  1
 0  1  0  2 X^2+1 X^2+3  1 X^2 X^2+2  1  3  1  1  X X^2+X X^2+X+2  1  1 X+1 X+3  X  2 X^2 X+2  1  1 X^2+X+1 X^2 X^2+2 X^2+X+3  X X+1  3  2 X^2+X+3 X^2+X+1  X X^2+X+2  1 X^2+1 X+2  1  1 X^2+2 X^2 X^2+2 X+3 X^2+3  1 X^2+X  1 X^2+X+1  3  X X+1 X^2+3  0
 0  0  1 X+3 X+1  2 X^2+X+1  X  3  1 X+2  X  3  1 X^2+X X^2+3 X^2+3  X X+1 X^2  0  1  1 X+3 X^2 X^2+X+1  1 X^2+X+2 X^2+1 X+2  1 X^2+X+3 X^2+X X^2+X+1 X^2+X X^2+3 X^2  1 X^2+X+3 X^2+X+3  3 X^2+X X+1  1  1 X^2+X+1 X^2+3  1  3 X+1 X^2+2 X+3 X^2+2 X+3 X^2+X+2 X+1  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+80x^53+562x^54+564x^55+930x^56+572x^57+400x^58+248x^59+320x^60+140x^61+122x^62+48x^63+91x^64+8x^65+4x^66+4x^67+2x^72

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 0.188 seconds.