The generator matrix
1 0 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
generates a code of length 13 over Z7[X]/(X^2) who´s minimum homogenous weight is 72.
Homogenous weight enumerator: w(x)=1x^0+126x^72+420x^73+30x^77+756x^79+1050x^80+18x^84
The gray image is a linear code over GF(7) with n=91, k=4 and d=72.
This code was found by Heurico 1.16 in 0.000647 seconds.