The generator matrix

 1  0  0  1  1  1  2  1  1  1  1  0  2 X^2  1  1 X^2+X+2  X  1  1  1 X^2+X+2 X^2+X+2 X^2+X+2  1  0 X+2  1 X^2  X  1  1 X^2+2  1 X^2  1  1  2  1  1 X^2+X
 0  1  0  2 X^2+1 X^2+3  1 X^2 X^2+2  1  3  1  1  X X^2+X X^2+X+2  1  1  X X+1 X+3  2 X^2+X  1 X^2+X+2  1  1 X+3  1  X  3 X+1  1 X^2+1  1 X^2+X+1 X^2+X  1  2 X+1  1
 0  0  1 X+3 X+1  2 X^2+X+1  X  3  1 X+2  X  3  1 X^2+X X^2+3 X^2+3  X  0 X+1 X^2  1  1 X+1 X+3 X^2+1 X^2+2 X^2+X+2  2  1 X^2  1 X^2+X+2  3  3 X^2  2 X+3 X^2+X+1  0 X+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+456x^38+656x^39+870x^40+600x^41+588x^42+304x^43+305x^44+152x^45+132x^46+16x^47+15x^48+1x^52

The gray image is a code over GF(2) with n=328, k=12 and d=152.
This code was found by Heurico 1.16 in 3.81 seconds.