The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+40x^57+2x^58+16x^59+2x^60+2x^62+1x^64

The gray image is a code over GF(2) with n=456, k=6 and d=228.
This code was found by Heurico 1.16 in 0.109 seconds.