The generator matrix

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

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+30x^40+408x^41+30x^42+96x^43+32x^44+384x^45+32x^46+1x^48+8x^49+1x^50+1x^66

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.