The generator matrix

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

generates a code of length 40 over Z27 who´s minimum homogenous weight is 71.

Homogenous weight enumerator: w(x)=1x^0+576x^71+1344x^72+2274x^73+3852x^74+7090x^75+8328x^76+11622x^77+17290x^78+20748x^79+21252x^80+24906x^81+21864x^82+15432x^83+11342x^84+4920x^85+2436x^86+1322x^87+132x^88+186x^89+110x^90+54x^91+48x^92+18x^93

The gray image is a code over GF(3) with n=360, k=11 and d=213.
This code was found by Heurico 1.16 in 36.6 seconds.