The generator matrix

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

generates a code of length 36 over Z3[X]/(X^3) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+32x^60+30x^61+72x^62+130x^63+396x^64+318x^65+910x^66+2100x^67+1374x^68+4946x^69+7260x^70+4578x^71+9806x^72+10758x^73+4698x^74+6550x^75+4002x^76+462x^77+72x^78+216x^79+156x^80+70x^81+24x^82+6x^83+40x^84+22x^87+10x^90+6x^93+4x^96

The gray image is a linear code over GF(3) with n=324, k=10 and d=180.
This code was found by Heurico 1.16 in 4.69 seconds.