The generator matrix

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

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+40x^15+80x^20+124x^25+2500x^28+220x^30+160x^35

The gray image is a linear code over GF(5) with n=35, k=5 and d=15.
This code was found by Heurico 1.16 in 0.00106 seconds.