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
 0  7  0  7 21 21  0  7 21 14 14 14  0  7 21 14 42 42 42 42 21 42  7  0 14 28 28
 0  0  7 35 21 14 28 14  7 35  7 28 35 28  0 14  0  7 14 42 35 28 42 42 21 28 21

generates a code of length 27 over Z49 who´s minimum homogenous weight is 154.

Homogenous weight enumerator: w(x)=1x^0+114x^154+126x^161+2058x^162+66x^168+12x^175+24x^189

The gray image is a code over GF(7) with n=189, k=4 and d=154.
This code was found by Heurico 1.16 in 0.00424 seconds.