The generator matrix

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

generates a code of length 37 over Z3[X]/(X^2) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+276x^68+256x^69+354x^71+120x^72+306x^74+142x^75+240x^77+68x^78+186x^80+84x^81+90x^83+56x^84+6x^86+2x^90

The gray image is a linear code over GF(3) with n=111, k=7 and d=68.
This code was found by Heurico 1.16 in 60.9 seconds.