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 X^2+2  0 X^2  0  0 X^2 X^2+2  0  0 X^2 X^2+2  0  0 X^2 X^2+2  0 X^2  0 X^2 X^2  2  2 X^2 X^2 X^2  2  2 X^2  2  2 X^2+2  0 X^2+2  0 X^2+2  2 X^2+2  2 X^2 X^2+2  2  0 X^2+2  2 X^2+2  2  0 X^2  0 X^2+2  2 X^2+2 X^2  2 X^2  0
 0  0 X^2+2 X^2  0 X^2+2 X^2  0  0 X^2+2 X^2  0  0 X^2+2 X^2  0  2 X^2+2 X^2  2 X^2+2 X^2  0  0 X^2+2  2 X^2+2  2  0  2 X^2+2 X^2+2  2 X^2 X^2  2  0 X^2+2 X^2+2  2 X^2  2 X^2  2 X^2 X^2  2  2 X^2+2 X^2 X^2+2 X^2+2  2  0  0  0  0
 0  0  0  2  0  0  2  0  2  2  0  2  2  2  0  2  2  2  2  2  2  2  2  2  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  0  0  0  2  0  0  0  2  2  2  2  0  0  0
 0  0  0  0  2  2  2  2  2  2  0  2  0  0  2  0  0  0  0  0  2  2  2  2  2  0  0  0  2  2  2  0  2  0  2  0  0  0  0  2  2  2  2  2  0  2  0  0  0  0  2  2  2  0  2  0  2

generates a code of length 57 over Z4[X]/(X^3+2,2X) 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 4.23 seconds.