The generator matrix

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

generates a code of length 43 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+144x^39+443x^40+632x^41+525x^42+636x^43+663x^44+554x^45+291x^46+94x^47+42x^48+30x^49+15x^50+22x^51+2x^52+1x^54+1x^60

The gray image is a code over GF(2) with n=344, k=12 and d=156.
This code was found by Heurico 1.16 in 0.172 seconds.