The generator matrix

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

generates a code of length 37 over Z3[X]/(X^2) who´s minimum homogenous weight is 61.

Homogenous weight enumerator: w(x)=1x^0+156x^61+306x^62+614x^63+978x^64+1056x^65+1558x^66+1974x^67+1986x^68+2580x^69+3366x^70+3132x^71+3928x^72+4872x^73+4056x^74+4508x^75+5022x^76+3660x^77+3990x^78+3732x^79+2256x^80+1924x^81+1440x^82+864x^83+502x^84+294x^85+168x^86+68x^87+36x^88+12x^89+2x^90+2x^93+4x^96+2x^99

The gray image is a linear code over GF(3) with n=111, k=10 and d=61.
This code was found by Heurico 1.16 in 29.5 seconds.