The generator matrix

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

generates a code of length 50 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+157x^42+812x^43+2839x^44+5612x^45+11672x^46+20128x^47+29056x^48+39452x^49+41869x^50+39854x^51+30506x^52+19946x^53+11178x^54+5262x^55+2447x^56+872x^57+264x^58+134x^59+45x^60+22x^61+12x^62+2x^63+2x^64

The gray image is a code over GF(2) with n=400, k=18 and d=168.
This code was found by Heurico 1.16 in 412 seconds.