The generator matrix

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

generates a code of length 21 over Z5[X]/(X^2) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+480x^78+400x^79+48x^80+640x^83+200x^84+52x^85+880x^88+400x^89+16x^90+8x^100

The gray image is a linear code over GF(5) with n=105, k=5 and d=78.
This code was found by Heurico 1.16 in 0.0265 seconds.