The generator matrix
1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 X 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 X+5 1 3X 6X+1 3X+3
generates a code of length 19 over Z7[X]/(X^2) who´s minimum homogenous weight is 109.
Homogenous weight enumerator: w(x)=1x^0+420x^109+378x^110+18x^112+1050x^116+504x^117+30x^119
The gray image is a linear code over GF(7) with n=133, k=4 and d=109.
This code was found by Heurico 1.16 in 0.00124 seconds.