The generator matrix

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

generates a code of length 20 over Z5[X]/(X^2) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+140x^68+720x^69+1488x^70+1060x^71+500x^72+1680x^73+3240x^74+3088x^75+1320x^76+4000x^77+6720x^78+9360x^79+7680x^80+3180x^81+8000x^82+8960x^83+9180x^84+5740x^85+1940x^86+60x^90+52x^95+16x^100

The gray image is a linear code over GF(5) with n=100, k=7 and d=68.
This code was found by Heurico 1.16 in 45.6 seconds.