The generator matrix

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

generates a code of length 41 over Z4[X]/(X^3+2,2X) who�s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+2x^40+46x^41+3x^42+8x^43+2x^45+1x^48+1x^50

The gray image is a code over GF(2) with n=328, k=6 and d=160.
This code was found by Heurico 1.16 in 0.031 seconds.