The generator matrix

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

generates a code of length 41 over Z4[X]/(X^3+2,2X) 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.