The generator matrix

 1  0  1  1  1  1  1  0  1  1  1  1  1  1  1  0  1
 0  1  1 26 25 18 26  1 21 16 20 21  4  1 16  1 25
 0  0 24  0  3 21 24 24 15 18 24 18  9 12 15  6  3
 0  0  0  9  0 18  0  9  9 18  9  9  9  9 18  9 18
 0  0  0  0  9  9  9  0  0 18 18  9  0 18  0  9 18

generates a code of length 17 over Z27 who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+138x^26+66x^27+372x^28+684x^29+2220x^30+1194x^31+6918x^32+8656x^33+14112x^34+12804x^35+8612x^36+1698x^37+1242x^38+94x^39+120x^40+84x^41+20x^42+6x^45+8x^48

The gray image is a code over GF(3) with n=153, k=10 and d=78.
This code was found by Heurico 1.16 in 1.61 seconds.