The generator matrix

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

generates a code of length 37 over Z3[X]/(X^2) who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+24x^58+48x^59+220x^60+114x^61+378x^62+638x^63+486x^64+1128x^65+1372x^66+1158x^67+2904x^68+2582x^69+2034x^70+5022x^71+3906x^72+3078x^73+6492x^74+4710x^75+3030x^76+5820x^77+3414x^78+2106x^79+3348x^80+2006x^81+864x^82+966x^83+594x^84+216x^85+138x^86+152x^87+12x^88+58x^90+20x^93+4x^96+6x^99

The gray image is a linear code over GF(3) with n=111, k=10 and d=58.
This code was found by Heurico 1.16 in 49.1 seconds.