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

generates a code of length 54 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+205x^50+72x^51+274x^52+312x^53+355x^54+312x^55+262x^56+72x^57+133x^58+38x^60+9x^62+2x^66+1x^96

The gray image is a code over GF(2) with n=432, k=11 and d=200.
This code was found by Heurico 1.16 in 68.4 seconds.