The generator matrix

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

generates a code of length 27 over Z5[X]/(X^2) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+124x^80+440x^85+928x^90+1188x^95+500x^96+1888x^100+6000x^101+2512x^105+24000x^106+2876x^110+32000x^111+2652x^115+1772x^120+916x^125+304x^130+24x^135

The gray image is a linear code over GF(5) with n=135, k=7 and d=80.
This code was found by Heurico 1.16 in 7.58 seconds.