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

generates a code of length 41 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 37.

Homogenous weight enumerator: w(x)=1x^0+32x^37+32x^38+24x^39+226x^40+408x^41+220x^42+16x^43+28x^44+24x^45+4x^46+8x^47+1x^80

The gray image is a code over GF(2) with n=328, k=10 and d=148.
This code was found by Heurico 1.16 in 0.047 seconds.