The generator matrix

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

generates a code of length 57 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+348x^54+256x^55+396x^56+152x^57+376x^58+216x^59+208x^60+8x^61+54x^62+8x^63+17x^64+4x^66+2x^70+1x^72+1x^88

The gray image is a code over GF(2) with n=456, k=11 and d=216.
This code was found by Heurico 1.16 in 78.9 seconds.