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

generates a code of length 54 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+212x^52+128x^54+140x^56+28x^60+3x^64

The gray image is a code over GF(2) with n=432, k=9 and d=208.
This code was found by Heurico 1.16 in 0.265 seconds.