The generator matrix

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

generates a code of length 26 over Z5[X]/(X^2) who´s minimum homogenous weight is 89.

Homogenous weight enumerator: w(x)=1x^0+680x^89+1956x^90+2880x^91+1900x^92+560x^93+5280x^94+7624x^95+10100x^96+7680x^97+2520x^98+19080x^99+24628x^100+24120x^101+23160x^102+7280x^103+48280x^104+50016x^105+39440x^106+31040x^107+7140x^108+31680x^109+23768x^110+15960x^111+3720x^112+72x^115+24x^120+24x^125+12x^130

The gray image is a linear code over GF(5) with n=130, k=8 and d=89.
This code was found by Heurico 1.16 in 85.7 seconds.