The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+168x^71+250x^72+780x^73+1290x^74+1844x^75+3102x^76+3858x^77+4584x^78+8718x^79+7830x^80+7098x^81+9222x^82+4992x^83+2672x^84+1344x^85+570x^86+186x^87+120x^88+174x^89+112x^90+42x^91+72x^92+20x^93

The gray image is a code over GF(3) with n=360, k=10 and d=213.
This code was found by Heurico 1.16 in 5.37 seconds.