The generator matrix

 1  0  1  1  1  1  1 21  1  1  1 24  0  1  1  1  1  1 21 24  1  1 21  1  1  1 24  1  1  1  1
 0  1  7 26 21  4 20  1 24 19 23  1  1  0 16 26  4 20  1  1 19 23  1 16 21 26  1 20  0 26  0
 0  0  9  0  0  0 18 18  9  9  9  0  9  0  9  9 18 18 18 18 18  0  0 18  9  0 18 18  0 18 18
 0  0  0  9  0  0 18 18 18  0  9  9 18  9 18 18 18  9  0  0 18 18  0  9  9  0  0  9 18  0 18
 0  0  0  0 18  0 18  9  9 18 18  9  0  0 18  9 18  0 18  0  0 18  9 18  0  9  9  0 18  0  0
 0  0  0  0  0  9 18  0 18 18 18 18 18 18  9  0  0 18  9  0 18  0  0  9  0 18  9  0 18  0 18

generates a code of length 31 over Z27 who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+78x^51+24x^52+66x^53+346x^54+120x^55+828x^56+1300x^57+2676x^58+4158x^59+4996x^60+10080x^61+8112x^62+7234x^63+10140x^64+5598x^65+2452x^66+240x^67+162x^68+244x^69+48x^70+30x^71+58x^72+28x^75+28x^78+2x^81

The gray image is a code over GF(3) with n=279, k=10 and d=153.
This code was found by Heurico 1.16 in 3.93 seconds.