The generator matrix

 1  0  0  0  1  1  1
 0  1  0  0 3X+1 3X+2  X
 0  0  1  0 3X+3 3X+2 2X
 0  0  0  1 3X+3 3X+4  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+40x^15+700x^16+400x^17+2580x^20+5400x^21+3800x^22+27500x^24+26124x^25+17100x^26+11200x^27+100000x^28+110000x^29+49220x^30+26800x^31+9600x^32+160x^35

The gray image is a linear code over GF(5) with n=35, k=8 and d=15.
This code was found by Heurico 1.16 in 4.93 seconds.