The generator matrix

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

generates a code of length 32 over Z27 who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+26x^51+24x^53+154x^54+54x^55+108x^56+284x^57+378x^58+168x^59+588x^60+1188x^61+3288x^62+862x^63+2322x^64+6144x^65+922x^66+1728x^67+318x^68+564x^69+108x^70+144x^71+142x^72+54x^73+12x^74+52x^75+28x^78+20x^81+2x^84

The gray image is a code over GF(3) with n=288, k=9 and d=153.
This code was found by Heurico 1.16 in 0.902 seconds.