The generator matrix

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

generates a code of length 20 over Z5[X]/(X^2) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+124x^70+168x^75+500x^76+124x^80+2000x^81+64x^85+84x^90+40x^95+20x^100

The gray image is a linear code over GF(5) with n=100, k=5 and d=70.
This code was found by Heurico 1.16 in 0.0115 seconds.