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 X^2+2  1  1  1  1  1  1 X^2 X^2  1  1  1  1  2  2  X  X  X  2  1
 0  X  0  X  2  0 X^2+X X^2+X+2  0  2 X+2 X+2  0 X^2+X+2 X^2+2  X X^2+2 X^2+X X^2+X+2  2  2 X^2+X+2  X X^2+X X^2+X X+2 X^2 X^2+X X^2  X X^2+2 X^2+X X^2 X^2  2  X  X X^2+X+2 X^2  0  2 X^2+X
 0  0  X  X  0 X^2+X+2 X^2+X  2 X^2 X^2+X+2 X^2+X+2 X^2 X^2+2 X^2  X  X X^2+X+2 X+2  X X+2 X^2+2 X^2+2 X^2+2 X^2+2  0  2  X X^2 X+2  X  X X^2+X  0  2  0 X^2+2  0  X  X X+2  X X+2
 0  0  0 X^2 X^2+2 X^2  2 X^2 X^2  0 X^2 X^2+2  0  0 X^2+2  2 X^2 X^2+2  2 X^2  2  0 X^2+2  2  2 X^2  2 X^2+2  0  0  2 X^2  0 X^2 X^2  0 X^2+2  0 X^2+2  0 X^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+426x^38+104x^39+688x^40+416x^41+948x^42+400x^43+616x^44+96x^45+268x^46+8x^47+102x^48+20x^50+2x^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 58.1 seconds.