The generator matrix

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

generates a code of length 15 over Z7[X]/(X^2) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+66x^70+168x^73+426x^77+1176x^78+1260x^80+6582x^84+14112x^85+5208x^87+37644x^91+42336x^92+7770x^94+672x^98+228x^105

The gray image is a linear code over GF(7) with n=105, k=6 and d=70.
This code was found by Heurico 1.16 in 0.89 seconds.