The generator matrix

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

generates a code of length 32 over Z7[X]/(X^2) who´s minimum homogenous weight is 182.

Homogenous weight enumerator: w(x)=1x^0+2088x^182+5502x^189+9174x^196+24x^210+18x^217

The gray image is a linear code over GF(7) with n=224, k=5 and d=182.
This code was found by Heurico 1.16 in 0.0518 seconds.