The generator matrix

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

generates a code of length 23 over Z7[X]/(X^2) who´s minimum homogenous weight is 126.

Homogenous weight enumerator: w(x)=1x^0+42x^126+138x^133+2058x^138+102x^140+6x^147+24x^154+30x^161

The gray image is a linear code over GF(7) with n=161, k=4 and d=126.
This code was found by Heurico 1.16 in 0.00318 seconds.