The generator matrix

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

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+244x^52+128x^53+344x^54+128x^55+130x^56+24x^58+24x^60+1x^96

The gray image is a code over GF(2) with n=432, k=10 and d=208.
This code was found by Heurico 1.16 in 0.265 seconds.