The generator matrix

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

generates a code of length 20 over Z5[X]/(X^2) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+240x^66+220x^68+400x^69+1108x^70+1460x^71+200x^72+2640x^73+1800x^74+2228x^75+4180x^76+1600x^77+10560x^78+5200x^79+5548x^80+10300x^81+3200x^82+14080x^83+5100x^84+4108x^85+3820x^86+48x^90+80x^95+4x^100

The gray image is a linear code over GF(5) with n=100, k=7 and d=66.
This code was found by Heurico 1.16 in 2.25 seconds.