The generator matrix

 1  0  0  1  1  1  2  0  1  1  2 X^2  1  1 X^2+X+2  1  1 X^2+X+2  X  1  1 X^2+X  1  1 X^2+X+2  X  1 X^2+2  1  1  1  1 X^2+2  1  1  X  0  1  1  1 X^2+X+2 X^2+X  1  1  1  1  1 X^2+2 X+2 X+2  1  2  1  0  1  1 X^2
 0  1  0  0 X^2+1 X^2+1  1 X^2+X  2 X^2+3  1  1 X^2+2  3 X+2 X+1  X  1  1 X^2+X+2 X+1  1 X^2+X X+2 X^2  1  3  1 X^2+X+1  1 X^2+X+3 X^2+X+2 X^2  3 X^2+X  1  1 X^2+2 X^2+3 X+1 X^2+X  1 X^2+2 X^2+X+2 X^2+X+2 X+3  0 X^2+X+2  1  1  2 X^2+2 X+3  1 X^2+X X+2 X^2+X+2
 0  0  1 X+1 X+3  2 X^2+X+3  1 X^2+X+2 X^2+1  1 X+2 X^2+3  X  1 X^2+2 X^2+X+1  1 X^2+X+2 X^2+2 X^2+1  0 X^2+1 X+2  1 X^2+X+3 X^2+X  2 X+1 X^2+2 X^2+3  2  1 X^2+1 X^2+3  3 X+2  2 X+1 X^2+2  1  X X^2+X+3 X^2+X+3 X^2+X  X X^2+X+1  1 X^2+X X^2 X^2+X+2  1  3 X^2+X+3  2  1  1
 0  0  0  2  2  0  2  2  2  0  0  2  0  2  0  2  0  2  2  0  0  0  2  2  0  0  0  2  0  2  2  2  2  2  0  0  2  2  0  0  2  0  0  2  0  2  2  0  0  2  0  2  2  0  0  0  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+482x^53+913x^54+1166x^55+1412x^56+1154x^57+930x^58+720x^59+545x^60+362x^61+222x^62+170x^63+65x^64+34x^65+6x^66+8x^67+1x^68+1x^70

The gray image is a code over GF(2) with n=456, k=13 and d=212.
This code was found by Heurico 1.16 in 0.625 seconds.