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

generates a code of length 61 over Z3[X]/(X^3) who´s minimum homogenous weight is 112.

Homogenous weight enumerator: w(x)=1x^0+270x^112+298x^114+690x^115+90x^116+552x^117+1224x^118+540x^119+1752x^120+2700x^121+3024x^122+3210x^123+2616x^124+720x^125+324x^126+510x^127+174x^129+378x^130+126x^132+270x^133+86x^135+66x^136+36x^138+18x^139+6x^142+2x^168

The gray image is a linear code over GF(3) with n=549, k=9 and d=336.
This code was found by Heurico 1.16 in 1.88 seconds.