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

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+30x^37+37x^38+62x^39+222x^40+346x^41+215x^42+40x^43+31x^44+22x^45+3x^46+10x^47+1x^48+2x^49+1x^50+1x^76

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 0.454 seconds.