The generator matrix

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

generates a code of length 32 over Z7[X]/(X^2) who´s minimum homogenous weight is 168.

Homogenous weight enumerator: w(x)=1x^0+72x^168+378x^174+912x^175+378x^176+798x^177+3276x^181+4188x^182+1806x^183+2016x^184+10836x^188+16002x^189+5544x^190+5922x^191+28728x^195+23748x^196+6678x^197+5670x^198+234x^203+288x^210+144x^217+30x^224

The gray image is a linear code over GF(7) with n=224, k=6 and d=168.
This code was found by Heurico 1.16 in 2.47 seconds.