The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+344x^51+226x^52+472x^53+64x^54+428x^55+212x^56+224x^57+52x^59+6x^60+8x^61+4x^63+1x^64+4x^67+2x^72

The gray image is a code over GF(2) with n=432, k=11 and d=204.
This code was found by Heurico 1.16 in 130 seconds.