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

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+2x^40+58x^41+157x^42+84x^43+154x^44+44x^45+2x^46+4x^47+3x^48+2x^49+1x^74

The gray image is a code over GF(2) with n=344, k=9 and d=160.
This code was found by Heurico 1.16 in 0.063 seconds.