The generator matrix

 1  0  0  1  1  1  1  1 5X  1  1  1  1  1  1
 0  1  0 5X+1  3 5X+2 5X 5X+3  1  6  1 4X+2 5X+6  4  5
 0  0  1 5X+5  3 5X+6 5X+1 5X+4 5X+2 X+3 X+2  X 4X+4  2 3X+5

generates a code of length 15 over Z7[X]/(X^2) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+630x^78+3780x^79+180x^84+7560x^85+18900x^86+24696x^90+90x^91+22680x^92+39060x^93+72x^105

The gray image is a linear code over GF(7) with n=105, k=6 and d=78.
This code was found by Heurico 1.16 in 0.587 seconds.