The generator matrix

 1  0  0  0  0  0  0  1  1  1  0  1  1  X  1  1  0  1  X  X  X  1
 0  1  0  0  0  0  0  X X+1  X  1  1  0  X  1 X+1  X  X  0  1  0  0
 0  0  1  0  0  0  0  0  1 X+1  X  1  X  1  0 X+1  0  1  0 X+1  1  0
 0  0  0  1  0  0  0  0  0  0  0  1 X+1  1  X  1  1  X  1  X  0  0
 0  0  0  0  1  0  0  1  0 X+1  X  X  1 X+1  0  X X+1  0 X+1  X  0  1
 0  0  0  0  0  1  0  1  X  X  1 X+1  0 X+1  0  0 X+1 X+1  1  X  1  1
 0  0  0  0  0  0  1  1 X+1  0  1  0  X  1  1  X  X  0  1  X  1  0

generates a code of length 22 over Z2[X]/(X^2) who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+34x^13+124x^14+304x^15+417x^16+572x^17+954x^18+1268x^19+1599x^20+1894x^21+1957x^22+1920x^23+1693x^24+1310x^25+937x^26+612x^27+365x^28+216x^29+123x^30+56x^31+21x^32+6x^33+1x^34

The gray image is a linear code over GF(2) with n=44, k=14 and d=13.
This code was found by Heurico 1.16 in 10.7 seconds.