The generator matrix

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

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+152x^49+178x^50+358x^51+369x^52+718x^53+732x^54+646x^55+367x^56+220x^57+83x^58+132x^59+47x^60+62x^61+12x^62+14x^63+2x^66+2x^67+1x^90

The gray image is a code over GF(2) with n=432, k=12 and d=196.
This code was found by Heurico 1.16 in 0.36 seconds.