The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  X  X  X  X  X  X  X  X  X  X  X  1  1  1  1  1  1  1  1  X  X X^2
 0 X^2+2  0 X^2+2  0 X^2+2  0 X^2+2  2 X^2  2 X^2  2 X^2  2 X^2 X^2+2 X^2+2 X^2+2 X^2+2  0  2  0  2 X^2 X^2  0  2 X^2 X^2  0  2 X^2+2 X^2  0  2 X^2+2 X^2  0  0  2
 0  0  2  0  0  2  2  2  2  2  2  2  0  0  0  0  0  0  2  2  0  0  2  2  2  0  2  2  2  0  0  0  0  0  0  0  2  2  0  2  2
 0  0  0  2  2  2  2  0  0  0  2  2  2  2  0  0  0  2  2  0  2  2  2  2  0  0  0  0  2  2  0  0  0  0  2  2  2  2  0  0  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+80x^40+128x^41+32x^42+8x^44+5x^48+2x^56

The gray image is a code over GF(2) with n=328, k=8 and d=160.
This code was found by Heurico 1.16 in 0.047 seconds.