The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  3  1  1  1  1  1  1  1
 0  9  0  0  0  0  9 18 18  0  0  9  9  9  9  9  9  9  0 18  0 18  0 18  0  9  9 18  9  0  9  0 18 18  9  0 18  9  0  9  0  9
 0  0  9  0  0  9 18  0 18  0  9  9 18 18  0  9  0  9  9  9  9  0  0 18 18  9 18  0  9 18 18  0  0 18  0 18  0  9 18 18 18  0
 0  0  0  9  0 18 18  9  0  9  9  0  0  9 18  9  9 18 18  0  0 18 18 18 18 18  0  0  9  9  9  9  0 18  0  9 18 18  0 18  0  0
 0  0  0  0  9 18 18 18 18 18  0 18  0  0 18 18  0  9  0  0 18 18  9 18  9 18 18  0  0  0  9  9  9  9  9  9  9  0  0  9  9  9

generates a code of length 42 over Z27 who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+82x^78+58x^81+162x^82+1458x^84+324x^85+58x^87+8x^90+20x^96+14x^99+2x^123

The gray image is a code over GF(3) with n=378, k=7 and d=234.
This code was found by Heurico 1.16 in 0.0439 seconds.