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

generates a code of length 23 over Z7[X]/(X^2) who´s minimum homogenous weight is 119.

Homogenous weight enumerator: w(x)=1x^0+168x^119+534x^126+426x^133+14406x^138+432x^140+432x^147+324x^154+84x^161

The gray image is a linear code over GF(7) with n=161, k=5 and d=119.
This code was found by Heurico 1.16 in 0.0878 seconds.