The generator matrix

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

generates a code of length 23 over Z5[X]/(X^2) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+232x^80+720x^81+1660x^82+1760x^83+1556x^85+3840x^86+5020x^87+2220x^88+5860x^90+10160x^91+9980x^92+5280x^93+7780x^95+10280x^96+8340x^97+3240x^98+104x^100+68x^105+24x^110

The gray image is a linear code over GF(5) with n=115, k=7 and d=80.
This code was found by Heurico 1.16 in 2.7 seconds.