The generator matrix

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

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+196x^80+980x^81+1200x^82+2100x^83+1340x^85+4860x^86+3400x^87+2700x^88+4888x^90+13340x^91+7100x^92+6300x^93+6532x^95+13320x^96+5800x^97+3900x^98+76x^100+56x^105+32x^110+4x^115

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 2.71 seconds.