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  3  1  1  3  1  1  1  3  3  1  1  1  1  3  1  3  1  9  3  1  1  1  1  1
 0  9  0  0  0  0  0  0  0  0  9 18 18  9  9  9  0 18  9 18  9  0 18  0  9  9  0 18  9 18 18 18  9  9  0  9 18 18  0  0  0  9 18  9  9  9  0  9  9  0 18 18  0  9  0 18 18 18  9  9  0  0  0  9  0 18  0  9  0  0
 0  0  9  0  0  0  0  9 18 18 18  0  0 18  9 18  9  0  9  9  0 18  9  0 18  9 18  0  9  0 18 18 18  9  0 18 18 18  9  9 18 18 18 18  0 18  0  0 18  9  9  0 18 18  9  0  0 18  9 18 18  9  0 18  9  0 18 18  0  0
 0  0  0  9  0  0  9 18  0 18  0  0 18  9  9 18  0  9  0 18  0 18 18  0 18  0  9 18 18  9  9  9 18  0 18  0 18  9  0 18  9 18 18  9  9  0  0 18  9 18  0 18 18  0  0 18  0  0 18 18  0  9  9  9  9  0 18  9  9  0
 0  0  0  0  9  0 18 18  9  0 18 18 18  0 18 18  0 18  9  0 18 18 18  9  0  0 18  9  0  9  0  9  0 18 18  0  0 18 18  9  0  9 18  9  0  9  0 18 18 18  9  0  9  9  9 18  9  0 18  9  9  9 18  0  0  9  9  0  9  9
 0  0  0  0  0  9 18 18 18 18 18 18  9 18  9  9 18  9 18 18 18 18  0 18  0  9  0  0 18  9 18  0 18  9  9  0  9  0  0  9  0  9 18  9 18  0  9  0  9  9  9  9 18  0  0  0  0 18 18  9  0  0  0  0  9 18  0  9 18 18

generates a code of length 70 over Z27 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+1530x^138+420x^139+2992x^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 code over GF(3) with n=630, k=8 and d=378.
This code was found by Heurico 1.16 in 0.52 seconds.