The generator matrix

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

generates a code of length 40 over Z3[X]/(X^2) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+154x^66+150x^67+342x^68+842x^69+678x^70+1068x^71+2112x^72+1734x^73+2232x^74+3042x^75+2580x^76+3024x^77+4380x^78+3984x^79+3588x^80+5312x^81+3888x^82+3654x^83+4766x^84+3042x^85+2520x^86+2462x^87+1224x^88+906x^89+774x^90+210x^91+162x^92+166x^93+6x^94+18x^96+18x^99+8x^102+2x^105

The gray image is a linear code over GF(3) with n=120, k=10 and d=66.
This code was found by Heurico 1.16 in 26 seconds.