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

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+44x^49+140x^50+92x^51+97x^52+440x^53+434x^54+440x^55+82x^56+92x^57+128x^58+44x^59+10x^60+2x^62+1x^64+1x^100

The gray image is a code over GF(2) with n=432, k=11 and d=196.
This code was found by Heurico 1.16 in 0.188 seconds.