The generator matrix

 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  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X
 0  0  X  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X
 0  0  0  X  0  0  0  0  0  0  0  0  0  X  X  X  0  0  0  0  X
 0  0  0  0  X  0  0  0  0  0  0  0  0  X  0  X  X  0  X  0  X
 0  0  0  0  0  X  0  0  0  0  0  0  0  X  X  0  X  X  0  X  X
 0  0  0  0  0  0  X  0  0  0  0  0  X  X  X  X  X  X  X  0  X
 0  0  0  0  0  0  0  X  0  0  0  0  X  0  0  X  X  0  0  X  0
 0  0  0  0  0  0  0  0  X  0  0  0  X  0  X  X  0  X  0  X  0
 0  0  0  0  0  0  0  0  0  X  0  0  X  0  X  0  X  0  X  X  0
 0  0  0  0  0  0  0  0  0  0  X  0  X  X  0  0  X  X  0  0  0
 0  0  0  0  0  0  0  0  0  0  0  X  X  X  0  X  0  X  X  X  0

generates a code of length 21 over Z2[X]/(X^2) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+45x^10+144x^12+240x^14+330x^16+520x^18+768x^20+4096x^21+768x^22+520x^24+330x^26+240x^28+144x^30+45x^32+1x^42

The gray image is a linear code over GF(2) with n=42, k=13 and d=10.
This code was found by Heurico 1.16 in 1.34 seconds.