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

generates a code of length 54 over Z4[X]/(X^2+2) who�s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+112x^51+46x^52+64x^53+32x^54+160x^55+44x^56+48x^59+2x^60+1x^64+2x^72

The gray image is a code over GF(2) with n=432, k=9 and d=204.
This code was found by Heurico 1.16 in 8.09 seconds.