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

generates a code of length 70 over Z49 who´s minimum homogenous weight is 378.

Homogenous weight enumerator: w(x)=1x^0+192x^378+696x^385+1440x^392+42x^396+1548x^399+1008x^403+1806x^406+9072x^410+1872x^413+36288x^417+1830x^420+54432x^424+1884x^427+1800x^434+1482x^441+1074x^448+816x^455+288x^462+78x^469

The gray image is a code over GF(7) with n=490, k=6 and d=378.
This code was found by Heurico 1.16 in 16.1 seconds.