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  1  1  1  X X^2  X  X  1
 0 X^2+2  0 X^2  0  0 X^2 X^2+2  0  0 X^2 X^2+2  0  2 X^2 X^2+2  2  2 X^2+2 X^2  2  2 X^2+2 X^2+2  2  2 X^2 X^2  2  0 X^2+2 X^2  0  2 X^2 X^2+2  2  0 X^2 X^2  0
 0  0 X^2+2 X^2  0 X^2+2 X^2  0  2 X^2 X^2+2  2  2 X^2  2 X^2+2  2 X^2+2 X^2+2  2  0 X^2+2 X^2  2  2 X^2 X^2+2  0  0 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2+2 X^2 X^2+2  0
 0  0  0  2  2  2  0  2  2  2  2  2  0  0  0  0  0  0  2  2  2  2  0  0  2  2  0  2  0  0  2  0  0  0  0  2  2  0  2  0  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+23x^38+24x^39+139x^40+148x^41+131x^42+16x^43+20x^44+4x^45+5x^46+1x^74

The gray image is a code over GF(2) with n=328, k=9 and d=152.
This code was found by Heurico 1.16 in 0.047 seconds.