The generator matrix

 1  0  0  1  1  1  1  1  1  1  1 18 21  0  1 21  1  1  1  9  1  1  1  1 15  1  1 18 24  1  1 15  0  1  1  1  1  1  1  0  1  1  1  1 15  3  1  1  3  1  1  1  1  1  1  1  1 12  1  1  1  1 15  1  1  1  9  1  1
 0  1  0  0 21 25 26 25  4 17 14  1  1 24 26  1 18 19  6  1 20 22 10  6  1  2  3  1 18  5 14  1  1  0 15 16  1 14 23  3  3 21 16 13  1  1 12 26  6  7 17 12 11 25 16 22 14  1 20 18 12 18  1  5 11 19  1  8 18
 0  0  1  7 14  2  8  1 24 12 19 25 14  1  0 18 12 15 10 11 17  8 19 11  1 16 11 24  1  5 24  2 22 22  6 21  2  4 11  1 17 12  8 10  5  4  9  4  1  9  4  6 18 25 10  2  0 14 14  1 16  3 24 12 22 24 24 12  3
 0  0  0  9 18 18 18  9  0  0  9  9 18  9  9  9 18 18  0  0  0  9  0  9  0 18  0 18 18  9 18  9 18 18  9 18 18  0 18  0 18  0  0  0 18  0 18  0 18  9  9 18  0  9 18  9  9  0  0  9  0  9  0 18  9  0  9 18  0

generates a code of length 69 over Z27 who´s minimum homogenous weight is 129.

Homogenous weight enumerator: w(x)=1x^0+226x^129+510x^130+1578x^131+2628x^132+2310x^133+4686x^134+4920x^135+4296x^136+6102x^137+5906x^138+4416x^139+5748x^140+4716x^141+2988x^142+3270x^143+2148x^144+900x^145+900x^146+540x^147+78x^148+54x^149+30x^150+30x^151+18x^152+8x^153+24x^154+18x^156

The gray image is a code over GF(3) with n=621, k=10 and d=387.
This code was found by Heurico 1.16 in 8.31 seconds.