The generator matrix

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

generates a code of length 32 over Z7[X]/(X^2) who´s minimum homogenous weight is 177.

Homogenous weight enumerator: w(x)=1x^0+1260x^177+168x^180+882x^181+1884x^182+6048x^183+8946x^184+1176x^186+2016x^187+4410x^188+4794x^189+9954x^190+13608x^191+7056x^193+6048x^194+9114x^195+7980x^196+14868x^197+17346x^198+42x^203+24x^210+24x^217

The gray image is a linear code over GF(7) with n=224, k=6 and d=177.
This code was found by Heurico 1.16 in 2.09 seconds.