The generator matrix

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

generates a code of length 15 over Z7[X]/(X^2) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+90x^84+420x^85+126x^86+534x^91+1050x^92+168x^93+12x^98

The gray image is a linear code over GF(7) with n=105, k=4 and d=84.
This code was found by Heurico 1.16 in 0.000836 seconds.