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

generates a code of length 32 over Z7[X]/(X^2) who´s minimum homogenous weight is 175.

Homogenous weight enumerator: w(x)=1x^0+432x^175+294x^180+522x^182+3528x^187+330x^189+10584x^194+414x^196+294x^203+240x^210+120x^217+48x^224

The gray image is a linear code over GF(7) with n=224, k=5 and d=175.
This code was found by Heurico 1.16 in 7.3 seconds.