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  1  1  1  1  1  1  1  1  1  1  1  3  3  0  3  1  1  1  0  1  1  3
 0  3 24  0 21 24  9  6 21 21 24  0  9 21 24  6  0  9 12 21  6 24  6 15 12 21  9 12 18 12 12 21 12 21 12 12  3 24 24  6  6 15 21  0  0  0  0  9 18  9 18  9 12  9 24  6 24 15 24  9 15  6  6  9  6  0 18 18 15 24  6 15  9  9  0  0  9 21 24  3 21 24 15 18  3 18  6 21
 0  0  9  0  0  0  0 18 18  9  9  9 18  9  0  9  9 18  0  9  0  9 18 18  0 18  9  9 18 18 18 18 18  9  0  0  9  0  0 18  0  0 18  0  0  9 18 18 18 18 18  0 18  0  0  9  9 18  9  9 18 18 18  9  9  9  0  9  9 18  0 18 18  9  0  9  0 18 18  9 18 18  0  9 18 18  0 18
 0  0  0  9  0  0 18  0  0  0  0  0  9 18 18  9 18 18  9 18  9 18 18  9 18  9  9  9  0 18  9 18  0  0  9 18  9  0  9  0  0 18 18  0  9 18 18 18  0  0  9 18 18  0  9 18  0  0 18  0  9  9 18 18  9  9 18  0  9  9 18 18  9  9  0  0  9  9  0 18  0  9  0 18  0 18  0 18
 0  0  0  0 18 18  0  9 18  9 18  9 18  0 18  0  9 18  0  9 18  0  9  9  0 18  9  9 18 18  9  9  9  0 18 18  0  0  0  0  9  0  0  9 18 18  9  0  9  0  9 18  0 18  9 18  9 18  9  0  0 18 18  0  9  0  9 18 18  9  9  0  0 18 18  0  9  9  0 18  9 18  0  9  0 18 18  0

generates a code of length 88 over Z27 who´s minimum homogenous weight is 168.

Homogenous weight enumerator: w(x)=1x^0+268x^168+108x^169+126x^170+238x^171+270x^172+396x^173+664x^174+648x^175+810x^176+1100x^177+864x^178+576x^179+102x^180+36x^182+78x^183+122x^186+64x^189+54x^190+30x^192+4x^204+2x^246

The gray image is a code over GF(3) with n=792, k=8 and d=504.
This code was found by Heurico 1.16 in 0.762 seconds.