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

generates a code of length 70 over Z3[X]/(X^2) who´s minimum homogenous weight is 126.

Homogenous weight enumerator: w(x)=1x^0+26x^126+110x^129+24x^130+112x^132+126x^133+90x^135+216x^136+72x^138+420x^139+76x^141+360x^142+50x^144+270x^145+40x^147+42x^148+40x^150+32x^153+16x^156+12x^159+24x^162+12x^165+8x^168+2x^171+2x^174+2x^177+2x^186

The gray image is a linear code over GF(3) with n=210, k=7 and d=126.
This code was found by Heurico 1.16 in 0.19 seconds.