The generator matrix

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

generates a code of length 57 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+606x^53+630x^54+1514x^55+930x^56+1622x^57+641x^58+876x^59+464x^60+494x^61+116x^62+198x^63+26x^64+62x^65+5x^66+4x^67+2x^68+1x^72

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 367 seconds.