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  1  1  1  1  1  1  X
 0  2  0 2X+2  0  0 2X+2  2  0  0 2X+2  2  0  0 2X+2  2  0 2X+2  0 2X+2 2X+2 2X 2X 2X+2 2X+2 2X+2 2X 2X 2X+2 2X 2X  2  0  2  0  2 2X  2 2X 2X+2  2 2X  0  2 2X  2 2X  0 2X+2  0  2 2X  2 2X+2 2X 2X+2  0
 0  0  2 2X+2  0  2 2X+2  0  0  2 2X+2  0  0  2 2X+2  0 2X  2 2X+2 2X  2 2X+2  0  0  2 2X  2 2X  0 2X  2  2 2X 2X+2 2X+2 2X  0  2  2 2X 2X+2 2X 2X+2 2X 2X+2 2X+2 2X 2X  2 2X+2  2  2 2X  0  0  0  0
 0  0  0 2X  0  0 2X  0 2X 2X  0 2X 2X 2X  0 2X 2X 2X 2X 2X 2X 2X 2X 2X  0  0  0  0  0  0  0  0  0  0  0  0 2X 2X 2X 2X 2X 2X 2X  0  0  0 2X  0  0  0 2X 2X 2X 2X  0  0  0
 0  0  0  0 2X 2X 2X 2X 2X 2X  0 2X  0  0 2X  0  0  0  0  0 2X 2X 2X 2X 2X  0  0  0 2X 2X 2X  0 2X  0 2X  0  0  0  0 2X 2X 2X 2X 2X  0 2X  0  0  0  0 2X 2X 2X  0 2X  0 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+52x^54+78x^56+768x^57+72x^58+48x^60+4x^62+1x^112

The gray image is a code over GF(2) with n=456, k=10 and d=216.
This code was found by Heurico 1.16 in 4.25 seconds.