The generator matrix

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

generates a code of length 39 over Z27 who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+504x^69+720x^70+2490x^71+3574x^72+6216x^73+9846x^74+9820x^75+17412x^76+21810x^77+20530x^78+28080x^79+24048x^80+13600x^81+9504x^82+5754x^83+1970x^84+696x^85+168x^86+242x^87+54x^88+30x^89+60x^90+12x^91+6x^92

The gray image is a code over GF(3) with n=351, k=11 and d=207.
This code was found by Heurico 1.16 in 35.9 seconds.