The generator matrix

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

generates a code of length 40 over Z3[X]/(X^2) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+60x^60+224x^63+328x^66+444x^69+54x^70+562x^72+540x^73+718x^75+2160x^76+724x^78+4320x^79+760x^81+4320x^82+882x^84+1728x^85+696x^87+544x^90+314x^93+174x^96+92x^99+26x^102+8x^105+4x^108

The gray image is a linear code over GF(3) with n=120, k=9 and d=60.
This code was found by Heurico 1.16 in 5.67 seconds.