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 1 1 1 X 1 1 X X 1 1 1 1 X X 1
0 X 0 0 0 0 0 0 0 0 0 0 0 0 X 2X 2X X 2X 2X 2X X X 2X X 2X 0 2X X 2X X 0 X 2X 2X 0 0 2X 0 2X X 2X 2X 0 2X 2X X X 0 2X 0 X X 2X 0 X 2X X X 0 X X 0 X X 0 X
0 0 X 0 0 0 0 0 0 0 0 X 2X 2X 2X 2X 0 X 0 X X 2X X 2X 0 X 2X 0 2X 0 X X 0 2X 2X X 2X X 2X X X 2X 0 X 2X 0 X X 2X 0 2X 0 0 0 X 2X 2X 2X 2X 0 X 0 X 0 2X X X
0 0 0 X 0 0 0 0 X 2X 2X 2X 0 0 X 0 X 2X X 2X 2X 2X 2X 0 0 0 2X 2X 0 X X X X 2X X 2X X X 2X X 0 X 0 0 2X 2X 2X 2X 2X 0 0 0 0 2X X 0 2X 2X X X 2X 0 2X 2X 2X 0 0
0 0 0 0 X 0 0 X 2X 0 2X 0 0 2X 2X X X X 2X X 0 2X X 2X X 0 X 2X 0 X 0 0 0 2X X 2X X X X 2X X X 0 2X X X X 2X 2X 0 2X 2X X X X X X 0 2X 2X 0 X 2X X 0 2X 0
0 0 0 0 0 X 0 2X 2X X 0 2X 2X 2X 2X 2X 2X 0 X 0 0 2X 2X 0 2X X 2X 0 0 X 2X X 2X X 2X 2X 2X 2X 2X 0 X X 0 2X X 0 0 0 X X 0 0 X 0 0 2X 2X 0 0 2X 0 X 2X 0 0 X 0
0 0 0 0 0 0 X 2X 2X 2X 2X 2X 2X X X X 0 2X 0 0 X 0 2X 2X 2X 0 X X 0 X 0 0 2X X 0 X 0 2X 0 2X 0 0 X 0 X X 0 X 2X 0 2X 0 2X 2X X 2X 2X 0 0 0 2X X 2X X X X 2X
generates a code of length 67 over Z3[X]/(X^2) who´s minimum homogenous weight is 117.
Homogenous weight enumerator: w(x)=1x^0+104x^117+202x^120+204x^123+18x^124+250x^126+180x^127+196x^129+720x^130+190x^132+1440x^133+170x^135+1440x^136+160x^138+576x^139+190x^141+158x^144+94x^147+94x^150+84x^153+42x^156+22x^159+16x^162+6x^165+2x^174+2x^186
The gray image is a linear code over GF(3) with n=201, k=8 and d=117.
This code was found by Heurico 1.16 in 1.37 seconds.