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

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

Homogenous weight enumerator: w(x)=1x^0+6x^40+110x^41+6x^42+1x^48+2x^49+2x^50

The gray image is a code over GF(2) with n=328, k=7 and d=160.
This code was found by Heurico 1.16 in 0.047 seconds.