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.