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

generates a code of length 61 over Z3[X]/(X^3) who´s minimum homogenous weight is 114.

Homogenous weight enumerator: w(x)=1x^0+152x^114+102x^115+72x^116+288x^117+114x^118+432x^119+228x^120+90x^121+3780x^122+174x^123+48x^124+576x^125+134x^126+42x^127+84x^129+18x^130+68x^132+66x^133+72x^135+6x^136+8x^138+2x^141+2x^147+2x^174

The gray image is a linear code over GF(3) with n=549, k=8 and d=342.
This code was found by Heurico 1.16 in 0.334 seconds.