The generator matrix

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

generates a code of length 41 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+80x^39+64x^40+232x^41+56x^42+64x^43+5x^44+8x^45+1x^48+1x^68

The gray image is a code over GF(2) with n=328, k=9 and d=156.
This code was found by Heurico 1.16 in 0.047 seconds.