The generator matrix

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

generates a code of length 54 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+158x^49+217x^50+408x^51+413x^52+656x^53+564x^54+592x^55+411x^56+290x^57+118x^58+124x^59+55x^60+48x^61+12x^62+28x^63+1x^82

The gray image is a code over GF(2) with n=432, k=12 and d=196.
This code was found by Heurico 1.16 in 0.359 seconds.