The generator matrix

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

generates a code of length 40 over Z3[X]/(X^2) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+198x^68+234x^69+174x^70+510x^71+610x^72+444x^73+990x^74+904x^75+720x^76+1590x^77+1202x^78+840x^79+1902x^80+1446x^81+1146x^82+1842x^83+1230x^84+738x^85+1182x^86+622x^87+282x^88+450x^89+204x^90+30x^91+84x^92+54x^93+28x^96+14x^99+8x^102+2x^105+2x^108

The gray image is a linear code over GF(3) with n=120, k=9 and d=68.
This code was found by Heurico 1.16 in 24.7 seconds.