The generator matrix

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

generates a code of length 7 over Z5[X]/(X^2) who´s minimum homogenous weight is 15.

Homogenous weight enumerator: w(x)=1x^0+20x^15+80x^16+60x^17+880x^20+960x^21+420x^22+5000x^24+6544x^25+3840x^26+980x^27+20000x^28+20000x^29+13060x^30+5120x^31+1040x^32+120x^35

The gray image is a linear code over GF(5) with n=35, k=7 and d=15.
This code was found by Heurico 1.16 in 0.215 seconds.