The generator matrix

 1  1  1  1  1
 0  X  0  0  0
 0  0  X  0  0
 0  0  0  X  0
 0  0  0  0  X

generates a code of length 5 over Z7[X]/(X^2) who´s minimum homogenous weight is 7.

Homogenous weight enumerator: w(x)=1x^0+30x^7+360x^14+2160x^21+6480x^28+100842x^30+7776x^35

The gray image is a linear code over GF(7) with n=35, k=6 and d=7.
This code was found by Heurico 1.16 in 0.114 seconds.