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 X^2+2  1  1
 0  X  0  X  2  0 X+2  X X^2 X^2+X X^2 X^2+X X^2+2 X^2 X^2+X+2 X^2+X  0  2  X X+2 X^2  0 X^2+X+2 X^2+X+2  X X^2+2 X^2 X^2+X+2 X^2+X+2 X+2 X^2 X^2+2  2 X^2 X^2+X+2  0 X^2+2 X+2  X X^2+2  X X^2+X  X
 0  0  X  X X^2 X^2+X X^2+X X^2 X^2 X^2+X+2  X  2  0 X^2+X X+2 X^2+2  2 X^2+X+2 X+2  0  2 X+2 X^2+X X^2 X^2+X X^2 X^2+X+2  0  X X^2+2 X+2 X+2  2 X^2+2  2 X^2+X+2  2 X+2 X^2+2 X^2+X  0 X^2 X^2+X+2

generates a code of length 43 over Z4[X]/(X^3+2,2X) 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.