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

generates a code of length 66 over Z3[X]/(X^3) who´s minimum homogenous weight is 124.

Homogenous weight enumerator: w(x)=1x^0+270x^124+54x^126+282x^127+48x^129+234x^130+4920x^132+234x^133+32x^135+96x^136+24x^138+132x^139+12x^141+108x^142+10x^144+72x^145+30x^148+2x^198

The gray image is a linear code over GF(3) with n=594, k=8 and d=372.
This code was found by Heurico 1.16 in 24.8 seconds.