The generator matrix

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

generates a code of length 32 over Z27 who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+462x^56+484x^57+756x^58+1890x^59+3234x^60+3132x^61+5442x^62+7768x^63+9072x^64+9522x^65+8218x^66+4428x^67+2526x^68+1266x^69+108x^70+444x^71+160x^72+114x^74+10x^75+12x^77

The gray image is a code over GF(3) with n=288, k=10 and d=168.
This code was found by Heurico 1.16 in 4.12 seconds.