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  X  1  1  X  1  1  1  1  1  X  1  X  1  1  X
 0  X  0  0  0  0  0  0  0  0  X 2X 2X  X  X  X  0 2X  X 2X  X  0  X  0 2X  X  0 2X  X 2X 2X 2X  X  X  X  0 2X 2X  0  0  0  X 2X  X  X  X  0 2X  X 2X  X  X  X  X  0  0  0 2X  0  X 2X  0  0  X  X 2X  0  0
 0  0  X  0  0  0  0  X 2X 2X 2X  0  0 2X  X 2X  X  0  X  X  0 2X 2X  0  X  X 2X  0  X  0 2X 2X 2X  X 2X  0 2X 2X  X  X 2X 2X 2X 2X  0 2X  0 2X  0  X  X  0  0 2X 2X  X  0  0  X  0 2X  X  X 2X 2X  X 2X  0
 0  0  0  X  0  0  X 2X  0 2X  0  0 2X  X  X 2X  0  X  0 2X  0 2X 2X  0 2X  0  X 2X 2X  X  X  X 2X  0  0 2X 2X  X  0 2X  X 2X 2X  X  X  X  X 2X  0  0  0  0 2X  0 2X 2X  X 2X  0 2X  0 2X  X  0  0  X  X  0
 0  0  0  0  X  0 2X 2X  X  0 2X 2X 2X  0 2X 2X  0 2X  X  0 2X 2X  0  X 2X  0 2X  X  0  X  0  X  0 2X  0 2X  0 2X 2X  X  0  X 2X  X  0 2X 2X 2X  X  X  X  X  X  0 2X  X  0  0  0  0  0 2X 2X  0  X 2X  X  0
 0  0  0  0  0  X 2X 2X 2X 2X 2X 2X  X 2X  X  X 2X  X 2X 2X 2X 2X  0 2X  0  X  0  0 2X  X 2X  0 2X  X  0  X  X  0  0  X  0  X 2X  X 2X  X  X  0  X  X  X 2X  0  X  0  0  X  X  X  X  X  X 2X 2X  X  0  0  X

generates a code of length 68 over Z3[X]/(X^2) who´s minimum homogenous weight is 126.

Homogenous weight enumerator: w(x)=1x^0+274x^126+60x^129+240x^132+708x^135+480x^138+192x^141+142x^144+56x^153+30x^162+2x^171+2x^189

The gray image is a linear code over GF(3) with n=204, k=7 and d=126.
This code was found by Heurico 1.16 in 23.5 seconds.