The generator matrix

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

generates a code of length 15 over Z7[X]/(X^2) who´s minimum homogenous weight is 79.

Homogenous weight enumerator: w(x)=1x^0+630x^79+180x^84+3150x^86+6174x^90+90x^91+6510x^93+72x^105

The gray image is a linear code over GF(7) with n=105, k=5 and d=79.
This code was found by Heurico 1.16 in 2.5 seconds.