The generator matrix

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

generates a code of length 20 over Z7[X]/(X^2) who´s minimum homogenous weight is 110.

Homogenous weight enumerator: w(x)=1x^0+1008x^110+138x^112+1176x^114+2688x^117+84x^119+7056x^121+4536x^124+60x^126+36x^133+24x^140

The gray image is a linear code over GF(7) with n=140, k=5 and d=110.
This code was found by Heurico 1.16 in 0.0267 seconds.