The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X 2X  1  1  1  1  X  1  1  1  0  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1
 0  X  0 3X+2 2X+2 X+2  2  X 2X+2 3X+2  0 3X+2 2X 3X 2X+2  X 3X+2  X  0 3X+2  2 3X 2X X+2 2X+2  0  X 3X X+2  0 3X+2  X  X 2X  0  2 2X+2 X+2 X+2 3X  X  X 2X
 0  0  2  0 2X+2 2X+2 2X 2X+2 2X+2  0 2X  2 2X+2 2X+2 2X 2X  0  2  0  0 2X 2X  2 2X+2  2  2  0  2  2 2X+2  2  0  2 2X  2 2X+2  2 2X  0  0  0 2X 2X
 0  0  0 2X  0  0 2X 2X 2X  0 2X 2X 2X  0  0 2X 2X 2X  0 2X 2X  0  0  0 2X  0  0 2X 2X 2X  0 2X  0  0 2X  0  0  0  0  0 2X 2X 2X
 0  0  0  0 2X  0  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X  0  0  0  0 2X  0 2X  0 2X 2X  0  0 2X  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+130x^39+84x^40+206x^41+434x^42+390x^43+451x^44+174x^45+12x^46+86x^47+39x^48+34x^49+2x^50+2x^51+2x^53+1x^76

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 136 seconds.