The generator matrix

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

generates a code of length 37 over Z3[X]/(X^2) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+62x^60+144x^61+324x^62+692x^63+816x^64+870x^65+1968x^66+1608x^67+1908x^68+3144x^69+2778x^70+3150x^71+4748x^72+3588x^73+4362x^74+5532x^75+4110x^76+3834x^77+4818x^78+2904x^79+2196x^80+2274x^81+1266x^82+762x^83+678x^84+276x^85+90x^86+106x^87+6x^88+14x^90+12x^93+6x^96+2x^99

The gray image is a linear code over GF(3) with n=111, k=10 and d=60.
This code was found by Heurico 1.16 in 23.1 seconds.