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

generates a code of length 41 over Z3[X]/(X^3) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+156x^74+52x^75+300x^77+114x^78+738x^80+254x^81+2916x^82+1248x^83+242x^84+234x^86+24x^87+144x^89+16x^90+72x^92+8x^93+24x^95+6x^96+6x^99+4x^102+2x^117

The gray image is a linear code over GF(3) with n=369, k=8 and d=222.
This code was found by Heurico 1.16 in 1.55 seconds.