The generator matrix

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

generates a code of length 41 over Z3[X]/(X^3) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+168x^72+36x^73+180x^74+1030x^75+1296x^76+1440x^77+2804x^78+4662x^79+5292x^80+6784x^81+8982x^82+7704x^83+6834x^84+6426x^85+2880x^86+1308x^87+468x^88+560x^90+162x^93+24x^96+2x^99+2x^102+4x^105

The gray image is a linear code over GF(3) with n=369, k=10 and d=216.
This code was found by Heurico 1.16 in 5.5 seconds.