The generator matrix

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

generates a code of length 42 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+114x^38+124x^39+316x^40+200x^41+612x^42+216x^43+247x^44+72x^45+58x^46+28x^47+49x^48+8x^50+2x^52+1x^68

The gray image is a code over GF(2) with n=336, k=11 and d=152.
This code was found by Heurico 1.16 in 0.094 seconds.