The generator matrix

 1  0  1  1  1 3X+2  1  1  X  1 2X+2  1  1  1  1 3X+2  1  0  1  1 X+2  1  2  1 3X  1  2  1  0 3X+2  1  1 2X+2  1  X  1  1 3X  1 2X+2  2  0
 0  1 X+1 3X+2  3  1 2X+3 2X+2  1  X  1 X+3 2X+1 X+1  0  1 3X+2  1 X+1 2X  1 3X  1  2  1 3X+2  1 3X+1  1  1 2X+3 2X+3  1  2 2X+2  0  3  1 X+3  X  0  2
 0  0  2  0  0  0  0 2X 2X 2X 2X  2 2X  2  2  2 2X+2 2X+2 2X+2 2X+2 2X+2 2X+2 2X+2 2X 2X  0 2X 2X  0 2X  2 2X+2 2X  2  2  0  2 2X+2  0  0 2X+2  2
 0  0  0 2X+2 2X 2X+2  2 2X  2  2 2X 2X  0  2 2X+2 2X  0  2 2X+2 2X  2  2 2X 2X+2 2X  0 2X+2 2X+2  2  0  0  2  2  2  2 2X+2  2 2X  2 2X+2 2X+2 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+336x^38+256x^39+625x^40+504x^41+710x^42+552x^43+581x^44+200x^45+222x^46+24x^47+64x^48+10x^50+7x^52+2x^54+2x^56

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 2.77 seconds.