The generator matrix

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

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+44x^38+204x^39+225x^40+220x^41+90x^42+100x^43+84x^44+52x^45+2x^52+2x^58

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 0.031 seconds.