The generator matrix

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

generates a code of length 41 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+18x^36+92x^38+144x^40+512x^41+184x^42+21x^44+44x^46+7x^48+1x^76

The gray image is a code over GF(2) with n=328, k=10 and d=144.
This code was found by Heurico 1.16 in 0.046 seconds.