The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+74x^38+206x^39+204x^40+74x^41+187x^42+194x^43+66x^44+6x^45+10x^46+1x^50+1x^64

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 0.032 seconds.