The generator matrix

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

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+208x^53+72x^54+192x^55+309x^56+524x^57+328x^58+184x^59+40x^60+112x^61+16x^62+40x^63+1x^64+20x^65+1x^104

The gray image is a code over GF(2) with n=456, k=11 and d=212.
This code was found by Heurico 1.16 in 59.6 seconds.