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  2  X X^2
 0  X X^2+2 X^2+X  0 X^2+X X^2+2 X+2  0 X^2+X X+2 X^2+2  2 X^2+X+2 X^2 X+2  0 X^2+X X^2+2 X+2  0 X^2+X X^2+2 X+2 X^2+2 X^2+X  0 X+2  2 X^2+X+2 X^2  X  0 X^2+X X^2+2  X  2  2 X+2 X^2+X+2  2  0 X^2+2
 0  0  2  0  0  0  2  0  0  2  2  2  0  2  2  2  2  0  0  2  2  2  0  0  0  0  2  0  2  2  0  2  0  2  2  2  2  0  2  0  2  0  0
 0  0  0  2  0  0  0  2  2  2  2  2  2  0  2  0  2  0  0  2  2  2  2  2  0  2  0  0  0  0  2  0  2  0  2  0  0  0  0  0  0  2  2
 0  0  0  0  2  2  2  2  2  0  2  0  0  2  2  0  0  0  0  0  2  2  2  0  2  2  2  2  0  0  0  2  0  2  2  0  2  0  2  2  2  2  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+106x^40+96x^41+236x^42+192x^43+208x^44+96x^45+48x^46+36x^48+4x^50+1x^80

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 0.094 seconds.