The generator matrix

 1  0  1  1  1  1  1 21  1  1  1 18  1 21  1  1  1  0  1  1  1  3  1  1  1  1  1 24  1 24  1 18  1 18  1  1  3  1  1 24 21  1 15  1
 0  1  1 26  7 18 17  1 25 21 20  1 24  1 19 23 21  1  4 26 15  1 14 24 22  3 20  1 19  1 20  1 19  1 21  4 15 17 24  1  1 11  1  0
 0  0 24  0  0 21 21 18  3  6 15 21  9 15  0 18  0  6 15 24  3  3 12  6  3  3 18 24  6  9 15 21 18 12  6 12 21  3 24  9 15  3 21  9
 0  0  0  9  0 18  0  9 18  0  9  0  9  9  0  0  9 18  0 18  9 18  9 18 18  0 18  9  0  0 18  0 18  9  9  9  0  0  9  0 18  9  9  9
 0  0  0  0  9  0  0  0  0  0  0  9  9  9 18  0 18  9 18 18 18  9  9 18  9 18 18  0  9 18  0  0  9  9  9  0  9 18 18  9 18  0  0 18

generates a code of length 44 over Z27 who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+156x^78+156x^79+384x^80+1196x^81+768x^82+2196x^83+3698x^84+3120x^85+5790x^86+7120x^87+7428x^88+7812x^89+7436x^90+4182x^91+4008x^92+2494x^93+246x^94+150x^95+350x^96+102x^97+66x^98+120x^99+36x^100+6x^101+18x^102+4x^105+2x^108+2x^114+2x^117

The gray image is a code over GF(3) with n=396, k=10 and d=234.
This code was found by Heurico 1.16 in 6 seconds.