The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  1  1  X  1  1  2
 0  X  0 X^2+X X^2 X^2+X+2 X^2+2  X  0 X^2+X X^2+2 X+2  2  X X^2+2 X^2+X+2  X  0 X^2+X X^2+X X^2+2  2 X^2 X+2 X+2 X^2+X  0 X^2+X  0 X^2+2 X^2+2 X+2 X+2  2  2  2 X^2+2  0  X  X  X
 0  0 X^2+2  0 X^2+2 X^2  0 X^2  2  2  2  2 X^2 X^2+2 X^2 X^2+2 X^2  0  0 X^2+2  0 X^2 X^2  2 X^2+2 X^2  2  2 X^2+2 X^2+2  2  0 X^2+2  0  2 X^2+2 X^2 X^2+2 X^2+2  2 X^2+2
 0  0  0  2  2  0  2  2  0  2  2  0  0  2  2  0  0  2  0  2  0  2  0  2  0  2  2  0  2  0  0  2  2  0  0  2  0  0  0  0  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+80x^38+64x^39+369x^40+132x^41+196x^42+92x^43+33x^44+28x^45+20x^46+4x^47+4x^48+1x^76

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 0.11 seconds.