The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1  1  1  1  0  1  1  0  1  0  1 2X+2  X  1  1 2X+2  1  X  X 2X  1
 0  X  0  X 2X  0 3X  X 2X+2 3X+2 2X+2 X+2  2 2X+2 3X+2 3X+2  X 2X+2  X 2X 3X X+2 2X X+2 2X  X  0  2 X+2  X 3X+2  X  2  2 3X 3X+2 2X  X 3X X+2  0  2 2X+2
 0  0  X  X 2X+2 3X+2 3X+2 2X+2 2X+2 2X  X 3X  0 3X+2 X+2  2  X  X X+2 3X  X 3X+2 2X+2  0 2X  0  X 3X+2  X 2X 2X+2 3X+2 2X+2  X X+2 3X+2  2 3X 3X+2 2X+2 3X  X 2X
 0  0  0 2X 2X 2X  0 2X  0 2X 2X  0 2X  0 2X  0  0  0 2X 2X  0  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X  0  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+68x^39+214x^40+310x^41+294x^42+404x^43+278x^44+212x^45+114x^46+56x^47+35x^48+30x^49+23x^50+8x^51+1x^66

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 0.093 seconds.