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  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  1  1  1  1  7  1  1  1  7  1
 0  7  0  0  7  7 28 14 21  0  7 21 21 21 35 14 14  7 28 14 21 28  0  0 28  7  7 21  0 28 42 28  0 42 21 28 21 42  7 14 14  0 21 28 35 21 14  7 28 14  7 14 42  0 28 42 35 35  0 14 28  0 14  7 21 28  0 14 42 28 42  7  7 42  0 42  7 42
 0  0  7  0 35 28 21 35 42 21 21 21 35 35 28  0  0 21  7 28 14  7  7 35  0  7  7  7 35  0 35 14 28 28 28 21 14  7 28  7 28  0 21 14 14 14 42  0 14 35 35 42  0 21  7 42 35 14 42 28 21 35  0  7 42 28  7 14 28  0 35 21 42 42 14  0  7 28
 0  0  0  7 35  7 14 42 42 28  7  0 14 42 42 35  7 14 35  7  7 21 14 28 35 35 14  0 35 28 14 28 21 42 21  7 14 42 14 42 35 14 21 21  7 42 35 35 42 21 42 42  0 21 14 21  7 21 35 28 35  7 21  0  0 14 35  7  7 21  0 28 28 35  0 21 35 28

generates a code of length 78 over Z49 who´s minimum homogenous weight is 448.

Homogenous weight enumerator: w(x)=1x^0+408x^448+534x^455+294x^456+426x^462+3528x^463+312x^469+10584x^470+210x^476+126x^483+84x^490+96x^497+36x^504+90x^511+36x^518+24x^525+6x^532+6x^539+6x^546

The gray image is a code over GF(7) with n=546, k=5 and d=448.
This code was found by Heurico 1.16 in 47.3 seconds.