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

generates a code of length 42 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+18x^40+90x^41+57x^42+60x^43+12x^44+10x^45+6x^46+1x^52+1x^62

The gray image is a code over GF(2) with n=336, k=8 and d=160.
This code was found by Heurico 1.16 in 0.047 seconds.