The generator matrix

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

generates a code of length 41 over Z3[X]/(X^2) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+72x^66+12x^67+204x^68+342x^69+258x^70+804x^71+972x^72+672x^73+1746x^74+1746x^75+1470x^76+3642x^77+2930x^78+2292x^79+5358x^80+4292x^81+3156x^82+5796x^83+4294x^84+3000x^85+5118x^86+2790x^87+1554x^88+2586x^89+1556x^90+600x^91+882x^92+454x^93+108x^94+108x^95+144x^96+62x^99+22x^102+4x^105+2x^108

The gray image is a linear code over GF(3) with n=123, k=10 and d=66.
This code was found by Heurico 1.16 in 26 seconds.