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  X  1  1  1  1 X^2  X  X  X
 0 X^2+2  0 X^2+2  0 X^2+2  0 X^2+2  0 X^2+2  0 X^2+2  0 X^2+2  2 X^2  2 X^2  2 X^2  2 X^2  2 X^2  0 X^2+2  2 X^2  2 X^2  2 X^2 X^2+2  0 X^2+2  0 X^2+2 X^2+2 X^2+2 X^2+2  0
 0  0  2  0  0  0  2  0  0  2  0  2  2  2  2  2  2  2  2  2  0  0  0  0  2  2  2  2  0  0  0  0  0  0  0  0  2  2  0  2  0
 0  0  0  2  0  0  0  2  2  2  2  2  2  0  2  0  0  0  0  2  2  2  2  0  2  0  2  2  0  2  0  0  0  0  0  2  2  0  2  2  0
 0  0  0  0  2  2  2  2  2  0  0  2  0  2  2  0  0  2  2  2  0  0  2  0  2  0  0  0  2  2  0  2  0  0  2  2  0  0  2  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+30x^38+160x^40+128x^41+161x^42+30x^44+1x^50+1x^72

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.