The generator matrix

 1  0  1  1  1  1  1  0  1  1  1 15  1  1  1 24  1  3  1 12  1  1  1  1  1  1  1  1  1  1 24  1  1  1
 0  1  1 26 18 25 17  1  0 22 26  1  3 19 20  1  4  1  5  1 22  0 26  6  5 26 24 18 18  2  1 23  3 25
 0  0 24  0 18  0 21 24 18 21 15 12  3 24 18  0  9 21  0 15 15 15 12 18  9 24  3 15 24  6 18 12 12  6
 0  0  0  3 21 12 18  9 24  6 15  0 18 15 15  6 24 15  9  3  3  0  3 18 15  9 12 21  6 12 18  6  9  3

generates a code of length 34 over Z27 who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+546x^60+270x^61+720x^62+2242x^63+2754x^64+3564x^65+5070x^66+7992x^67+9828x^68+8292x^69+8694x^70+4680x^71+2662x^72+702x^73+162x^74+636x^75+216x^78+18x^81

The gray image is a code over GF(3) with n=306, k=10 and d=180.
This code was found by Heurico 1.16 in 4.44 seconds.