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

generates a code of length 57 over Z4[X]/(X^2+2) 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 60.1 seconds.