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

generates a code of length 54 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+72x^48+60x^50+32x^51+190x^52+352x^53+700x^54+352x^55+128x^56+32x^57+52x^58+40x^60+20x^62+6x^64+10x^68+1x^96

The gray image is a code over GF(2) with n=432, k=11 and d=192.
This code was found by Heurico 1.16 in 0.219 seconds.