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 2X+2  1  0  1  1  X  2  X  1  X  1  1  1  1  X  1  1 2X  X
 0  X  0  X  0 2X 3X+2  X 2X+2 3X+2 2X+2 X+2 2X+2  2 3X X+2 3X 2X+2  2 3X+2  0 2X  X 2X+2  2  X 3X+2  0 3X+2  X  X 3X 3X 3X 3X+2  2  2 2X+2  X  0 2X+2 3X+2
 0  0  X  X  2 X+2 3X+2 2X+2  2 2X  0  2  X 3X+2 3X+2  X 3X  X  0  2 3X  X  2  X 3X+2 2X  0  2 2X 3X+2  X 3X+2 3X+2  0  2 2X 2X+2 X+2 2X+2 3X+2  X X+2
 0  0  0 2X  0  0  0 2X 2X 2X 2X  0 2X 2X  0 2X  0 2X  0  0 2X 2X 2X  0  0 2X  0 2X  0  0 2X 2X 2X 2X 2X 2X  0 2X  0 2X  0  0
 0  0  0  0 2X 2X  0  0  0 2X 2X 2X  0 2X 2X 2X  0 2X  0  0  0  0 2X  0 2X  0 2X  0  0  0 2X  0 2X 2X 2X  0  0 2X  0  0 2X 2X

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

Homogenous weight enumerator: w(x)=1x^0+399x^38+96x^39+725x^40+416x^41+1000x^42+416x^43+531x^44+96x^45+276x^46+113x^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 28.5 seconds.