The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  3  1  1  0  1  1  3  1  3  1
 0  3  0  0  0 18  9 21  3 24  6 24 24 24 15  3 15 24  6 12  9 21 21 12  0  3 12  9  9 12  3  3
 0  0  3  0  9 21 21 15 12 12 15  3 15 18 24 15  0  3 18 24  6 18 24 18 24 12  0  0  3 15 21 24
 0  0  0  3 15 15 21  6 18  9 15 12 12  0 18  3  3 24 15  9  0 15  6  3  3 12  6 12  9  6 15 12

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

Homogenous weight enumerator: w(x)=1x^0+330x^56+260x^57+54x^58+828x^59+954x^60+324x^61+2286x^62+2434x^63+3564x^64+3882x^65+2368x^66+432x^67+930x^68+342x^69+396x^71+184x^72+90x^74+16x^75+6x^77+2x^84

The gray image is a code over GF(3) with n=288, k=9 and d=168.
This code was found by Heurico 1.16 in 1.71 seconds.