The generator matrix

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

generates a code of length 54 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 47.

Homogenous weight enumerator: w(x)=1x^0+346x^47+1372x^48+3754x^49+6463x^50+10550x^51+15133x^52+17950x^53+19576x^54+18440x^55+15414x^56+10774x^57+6197x^58+3096x^59+1179x^60+556x^61+172x^62+62x^63+19x^64+4x^65+4x^66+2x^67+2x^68+2x^69+2x^70+2x^74

The gray image is a code over GF(2) with n=432, k=17 and d=188.
This code was found by Heurico 1.16 in 114 seconds.