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

generates a code of length 41 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+109x^38+445x^40+358x^42+65x^44+45x^46+1x^76

The gray image is a code over GF(2) with n=328, k=10 and d=152.
This code was found by Heurico 1.16 in 0.062 seconds.