The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+152x^39+98x^40+310x^41+293x^42+414x^43+295x^44+252x^45+58x^46+116x^47+14x^48+24x^49+1x^50+6x^51+7x^52+4x^53+2x^57+1x^64

The gray image is a code over GF(2) with n=344, k=11 and d=156.
This code was found by Heurico 1.16 in 31.6 seconds.