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

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

Homogenous weight enumerator: w(x)=1x^0+16x^50+24x^51+35x^52+104x^53+148x^54+104x^55+43x^56+24x^57+11x^58+1x^60+1x^106

The gray image is a code over GF(2) with n=216, k=9 and d=100.
This code was found by Heurico 1.16 in 0.0723 seconds.