The generator matrix

 1  0  1  1  1  1  1  1  1  0  1  1  1  1  1  0  1  1  5  1  1  1  1  1  1  1  1  1  1  0  1  1  1 10  1  5  1  5  1  1  1  1  1  1  1  1  5  1  1  1  5  1  1  1  1  1 15  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0
 0  1  1  7 24 18 16  0  7  1 18 14  0 16 14  1  7 18  1  7 14  0 16 18 23 12  5 14 16  1  5 17  9  1  9  1 21  1 23  7 14 15  6 11 20 23  1 12 21  5  1  9 18 12 12 22  1  5 16 10  2 22 13 23 12 19  2 22  9  0  6 21 20  5  2 22  1  0
 0  0 15  0  0  0  0  5 10 15 10 15 10 20  0 10 10 10 10 15  5 10  0 10 10 15 15  5  5 15 20 15  0  5 20  5 10 10 20  0 15  0  5 20 20 20 10 20 10 20  5 10 20  0  0 20 15 20 15  0 10 10 10 15 20 10  0 15 10  0  5  0 15  0  5 20 15  5
 0  0  0  5  0  5 15 15  0 10 10 20 10 10 15  0 10  5  5  5  0 20 15 20  0 15 15  5 15  0 15  5 20  5  5 10 15 15  5 20  0 10 10 10 20 20 20 15 15  0  0  0 20  0 20  5  5 15 10 20 20  0 15 20  0 15 10  0 20  5  0 20  5 10  0 10  5  0
 0  0  0  0 15 15 10 20 20  5 20 20 10  0  0  0 15 10 15 10  5 10  5  5  5  0 20 20  5  5 15  5  5  5  5 10  5 10  0 20 20 20 20 15 20 10  0 10 15 20  5  0 15 15 15 15 20  5 10  5  5 15  0 15 15  0  0 10 15 10  5 10 10 10 20 10 15  5

generates a code of length 78 over Z25 who´s minimum homogenous weight is 290.

Homogenous weight enumerator: w(x)=1x^0+268x^290+300x^291+120x^292+180x^293+580x^294+388x^295+1320x^296+720x^297+520x^298+1320x^299+436x^300+2080x^301+1400x^302+1400x^303+3440x^304+408x^305+4500x^306+2360x^307+2400x^308+5440x^309+332x^310+5380x^311+2660x^312+4000x^313+7140x^314+288x^315+5780x^316+3040x^317+3020x^318+5560x^319+224x^320+4060x^321+1840x^322+980x^323+1520x^324+164x^325+1400x^326+360x^327+184x^330+180x^331+136x^335+100x^340+80x^345+64x^350+28x^355+12x^360+4x^365+8x^370

The gray image is a code over GF(5) with n=390, k=7 and d=290.
This code was found by Heurico 1.16 in 27 seconds.