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

generates a code of length 79 over Z49 who´s minimum homogenous weight is 448.

Homogenous weight enumerator: w(x)=1x^0+84x^448+474x^455+426x^462+2058x^468+414x^469+12348x^475+282x^476+186x^483+120x^490+150x^497+96x^504+24x^511+54x^518+48x^525+18x^532+18x^539+6x^546

The gray image is a code over GF(7) with n=553, k=5 and d=448.
This code was found by Heurico 1.16 in 0.438 seconds.