The generator matrix

 1  0  1  1  1 X+2  1  1 2X+2  1  1 3X  1  1 2X  1  1 3X+2  1  1  2  1  1  X  1  1  X  X  0  X  X 2X+2  1 2X+2  1 3X  X  X  1  1  1
 0  1 X+1 X+2  3  1 2X+2 3X+3  1 3X 2X+1  1 2X 3X+1  1 3X+2 2X+3  1  2 X+3  1  X  1  1  0 X+2 2X X+2  X  2 3X  X 3X+3  1 2X+1  1  0 2X+2 2X+2 3X 2X

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

Homogenous weight enumerator: w(x)=1x^0+111x^40+56x^41+46x^42+32x^43+8x^45+2x^46

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 0.015 seconds.