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

generates a code of length 41 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+18x^36+92x^38+144x^40+512x^41+184x^42+21x^44+44x^46+7x^48+1x^76

The gray image is a code over GF(2) with n=328, k=10 and d=144.
This code was found by Heurico 1.16 in 0.063 seconds.