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

generates a code of length 57 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+5x^52+20x^53+14x^54+32x^55+109x^56+664x^57+108x^58+32x^59+11x^60+20x^61+6x^62+1x^64+1x^112

The gray image is a code over GF(2) with n=456, k=10 and d=208.
This code was found by Heurico 1.16 in 0.171 seconds.