The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 2X+2  1  1
 0  X  0  X 2X  0 3X  X  2 X+2  2 X+2 2X+2  2 3X+2 X+2  0 2X  X 3X  2  0 3X+2 3X+2  X 2X+2  2 3X+2 3X+2 3X  2 2X+2 2X  2 3X+2  0 2X+2 3X  X 2X+2  X X+2  X
 0  0  X  X  2 X+2 X+2  2  2 3X+2  X 2X  0 X+2 3X 2X+2 2X 3X+2 3X  0 2X 3X X+2  2 X+2  2 3X+2  0  X 2X+2 3X 3X 2X 2X+2 2X 3X+2 2X 3X 2X+2 X+2  0  2 3X+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+60x^40+80x^41+151x^42+454x^43+138x^44+68x^45+65x^46+6x^47+1x^84

The gray image is a code over GF(2) with n=344, k=10 and d=160.
This code was found by Heurico 1.16 in 0.047 seconds.