The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+116x^50+3x^52+4x^54+3x^56+1x^60

The gray image is a code over GF(2) with n=400, k=7 and d=200.
This code was found by Heurico 1.16 in 0.047 seconds.