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

generates a code of length 42 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+42x^41+41x^42+26x^43+12x^44+2x^45+2x^47+1x^48+1x^54

The gray image is a code over GF(2) with n=336, k=7 and d=164.
This code was found by Heurico 1.16 in 0.031 seconds.