The generator matrix

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

generates a code of length 21 over Z2[X]/(X^2) who´s minimum homogenous weight is 11.

Homogenous weight enumerator: w(x)=1x^0+64x^11+225x^12+476x^13+858x^14+1468x^15+2380x^16+3598x^17+5117x^18+6688x^19+7754x^20+8056x^21+7692x^22+6696x^23+5268x^24+3836x^25+2570x^26+1440x^27+733x^28+412x^29+146x^30+28x^31+23x^32+6x^33+1x^34

The gray image is a linear code over GF(2) with n=42, k=16 and d=11.
This code was found by Heurico 1.11 in 21.5 seconds.