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  2  X  1
 0  X 2X+2 X+2  0 X+2 2X+2 3X  0 3X 2X+2 X+2  2 X+2 3X  0 2X X+2 2X+2 3X 3X+2  X  0  0 3X 2X+2  2 X+2 2X 3X+2  2  X  0 2X X+2 3X+2 2X+2 3X  2  X 2X+2 2X+2 3X 3X X+2 2X+2  X 3X  2 2X+2  2 2X+2 X+2  0
 0  0 2X  0  0  0  0  0  0  0  0  0 2X  0  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X  0 2X 2X 2X 2X 2X 2X  0 2X  0  0  0  0  0 2X  0 2X  0 2X  0 2X  0 2X 2X  0  0 2X 2X  0
 0  0  0 2X  0  0  0  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X  0 2X  0 2X  0 2X  0  0  0  0 2X 2X  0 2X  0  0 2X  0  0 2X 2X 2X 2X  0  0  0 2X  0  0  0  0 2X  0 2X
 0  0  0  0 2X  0  0 2X 2X 2X 2X 2X 2X 2X  0 2X  0  0  0 2X  0 2X 2X  0 2X  0  0  0 2X 2X 2X  0  0 2X  0 2X 2X  0  0  0  0  0 2X  0 2X 2X  0 2X 2X 2X 2X  0  0 2X
 0  0  0  0  0 2X 2X 2X 2X  0  0  0 2X 2X 2X 2X  0  0 2X  0 2X 2X  0  0 2X 2X 2X  0 2X  0  0 2X 2X  0  0 2X 2X 2X  0  0  0  0  0  0 2X  0 2X  0 2X  0 2X 2X 2X  0

generates a code of length 54 over Z4[X]/(X^2+2) 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.