The generator matrix
1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 1 0 1 1 1 1 0 1 1 1 1 X 1 1 1 1 1 1 1
0 1 1 2 0 1 2 1 0 2X+1 2 1 2X+1 0 2 1 X+1 X X+2 0 1 2 2 0 X 1 0 2X+1 2X+1 2X+1 1 X+2 X 2 X+2 2X+1 X 0
0 0 2X 0 0 0 0 0 0 0 0 0 0 X X 2X X X 2X X X X X X X 2X 0 2X 2X 2X 0 2X 2X X X 0 2X 0
0 0 0 X 0 0 0 0 X 2X X 2X X 2X 2X 0 0 0 2X 0 X 2X 2X X 2X 0 2X X 2X X X X X 0 2X X 2X 0
0 0 0 0 X 0 0 X 2X 2X X X 0 2X 2X 2X X 2X 2X 2X 0 X X X X 0 X 0 0 0 2X 0 0 0 2X 2X 0 0
0 0 0 0 0 2X 0 2X X 0 X X 2X 2X X 2X 0 0 0 X X X X 0 2X 2X 2X X 0 0 X 0 2X 0 0 X X X
0 0 0 0 0 0 X 2X 0 2X 2X X X 2X 2X X 0 2X X X X 2X 0 2X X 2X X X 2X 0 0 X 0 2X X 2X 2X 2X
generates a code of length 38 over Z3[X]/(X^2) who´s minimum homogenous weight is 60.
Homogenous weight enumerator: w(x)=1x^0+48x^60+6x^61+6x^62+160x^63+120x^64+138x^65+208x^66+390x^67+384x^68+252x^69+888x^70+1122x^71+218x^72+1740x^73+2226x^74+260x^75+2154x^76+2346x^77+270x^78+2094x^79+1842x^80+222x^81+1002x^82+606x^83+200x^84+318x^85+78x^86+162x^87+36x^88+126x^90+34x^93+24x^96+2x^99
The gray image is a linear code over GF(3) with n=114, k=9 and d=60.
This code was found by Heurico 1.16 in 3.31 seconds.