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  X  1  1  1
 0  X  0  0  0  0  0  X  X  X  X 4X  X  X 3X 2X 4X 2X 4X 2X  0 2X  X 3X  X  0
 0  0  X  0  0  0  X 3X 3X 2X 4X  X 2X  X  0 3X  0  X 4X  0  X 2X 4X  0 4X 4X
 0  0  0  X  0  0 3X 4X 3X 3X 4X  0  0 3X 3X 2X  0 4X 3X 4X  0 4X 3X 3X 3X 2X
 0  0  0  0  X  0 3X  0 2X 3X 2X 2X  X 2X 2X  0 2X 2X 3X 3X 3X  X 4X  X  0  X
 0  0  0  0  0  X 3X  X 2X  0 4X 4X 4X  X  0 4X 3X 2X 3X 4X 4X  X  X 4X 2X  X

generates a code of length 26 over Z5[X]/(X^2) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+276x^80+772x^85+1280x^90+1740x^95+15036x^100+52760x^105+2828x^110+2220x^115+940x^120+228x^125+44x^130

The gray image is a linear code over GF(5) with n=130, k=7 and d=80.
This code was found by Heurico 1.16 in 7.57 seconds.