The generator matrix

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

generates a code of length 43 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+322x^40+1020x^41+508x^42+864x^43+364x^44+524x^45+158x^46+152x^47+87x^48+64x^49+22x^50+10x^52

The gray image is a code over GF(2) with n=344, k=12 and d=160.
This code was found by Heurico 1.16 in 0.11 seconds.