The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1 X^2  1  0  1  1  X  0  X  1  X  1  1  1  1  X  1  1  2  X
 0  X  0  X  0  2 X^2+X  X X^2 X^2+X X^2 X^2+X+2 X^2 X^2+2 X+2 X^2+X+2 X+2 X^2 X^2+2 X^2+X  0  2  X X^2 X^2+2  X X^2+X  0 X^2+X  X X^2+X X+2 X^2+X+2 X+2 X^2+X X^2+2 X^2+2 X^2  X  0 X^2 X^2+X
 0  0  X  X X^2+2 X^2+X+2 X^2+X X^2 X^2+2  2  0 X^2+2  X X^2+X X^2+X  X X+2  X  0 X^2+2 X+2  X X^2+2  X X^2+X  2  0 X^2+2  2 X^2+X X^2+X X^2+X X+2  0 X^2+2  2 X^2 X^2+X+2 X^2 X^2+X  X X^2+X+2
 0  0  0  2  0  0  0  2  2  2  2  0  2  2  0  2  0  2  0  0  2  2  2  0  0  2  0  2  0  0  2  2  2  2  2  2  0  2  0  2  0  0
 0  0  0  0  2  2  0  0  0  2  2  2  0  2  2  2  0  2  0  0  0  0  2  0  2  0  2  0  0  0  2  0  2  2  2  0  0  2  0  0  2  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+403x^38+64x^39+761x^40+448x^41+928x^42+448x^43+555x^44+64x^45+280x^46+117x^48+20x^50+5x^52+1x^54+1x^64

The gray image is a code over GF(2) with n=336, k=12 and d=152.
This code was found by Heurico 1.16 in 7.5 seconds.