The generator matrix

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

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+241x^38+320x^39+360x^40+272x^41+330x^42+288x^43+180x^44+16x^45+29x^46+1x^48+8x^50+1x^52+1x^60

The gray image is a code over GF(2) with n=328, k=11 and d=152.
This code was found by Heurico 1.16 in 0.438 seconds.