The generator matrix

 1  0  0  1  1  1  1  1  1  1 21 18  1  1  1  1  0  1  1  1  1  1  1  1  1  3  1  6  1 18  1  1
 0  1  0  1 15 17  1 17 24 25  1  1 23 18  3 23  1 21 11 13  8 13  7 19 15  1  4  1  2  1  9  9
 0  0  1 26 16 20  1 21  2 24 10 17  1 13  2  6 21 18 25 13  0 17 24 25  6  7 17 13  7  0  9  0
 0  0  0 24 15 24  9  0 21  3 12 21  3 12  9 15 15  6  0 24 21  3 18 12 12 18  9  6  9  9 15  9

generates a code of length 32 over Z27 who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+264x^55+468x^56+1756x^57+3156x^58+4866x^59+7614x^60+11052x^61+18264x^62+21010x^63+27528x^64+31002x^65+21818x^66+14670x^67+7734x^68+3778x^69+1476x^70+312x^71+146x^72+162x^73+48x^74+6x^75+12x^76+2x^78+2x^81

The gray image is a code over GF(3) with n=288, k=11 and d=165.
This code was found by Heurico 1.16 in 27.6 seconds.