The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+271x^38+232x^39+608x^40+544x^41+845x^42+528x^43+577x^44+224x^45+217x^46+8x^47+27x^48+3x^50+2x^52+8x^54+1x^60

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 0.938 seconds.