The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+386x^54+204x^55+438x^56+140x^57+369x^58+140x^59+262x^60+20x^61+52x^62+8x^63+16x^64+9x^66+3x^72

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 0.172 seconds.