The generator matrix

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

generates a code of length 42 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+260x^39+337x^40+340x^41+281x^42+340x^43+214x^44+156x^45+54x^46+48x^47+6x^48+1x^50+8x^51+2x^56

The gray image is a code over GF(2) with n=336, k=11 and d=156.
This code was found by Heurico 1.16 in 91.9 seconds.