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

generates a code of length 54 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+224x^50+16x^51+274x^52+240x^53+554x^54+240x^55+262x^56+16x^57+206x^58+6x^60+6x^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 7.61 seconds.