The generator matrix

 1  1  1  1  1
 0  X  0  0  X
 0  0  X  0 5X
 0  0  0  X 5X

generates a code of length 5 over Z7[X]/(X^2) who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+60x^14+300x^21+930x^28+14406x^30+1110x^35

The gray image is a linear code over GF(7) with n=35, k=5 and d=14.
This code was found by Heurico 1.16 in 0.00406 seconds.