The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0 X^2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2  0
 0  0 X^2  0  0  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0
 0  0  0 X^2  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2  0  0  0  0 X^2  0
 0  0  0  0 X^2  0  0  0  0  0  0  0  0 X^2  0 X^2 X^2  0 X^2  0 X^2  0
 0  0  0  0  0 X^2  0  0  0  0  0  0  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0
 0  0  0  0  0  0 X^2  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0
 0  0  0  0  0  0  0 X^2  0  0  0  0 X^2  0  0 X^2 X^2  0  0 X^2  0  0
 0  0  0  0  0  0  0  0 X^2  0  0  0 X^2  0 X^2 X^2  0 X^2  0 X^2  0  0
 0  0  0  0  0  0  0  0  0 X^2  0  0 X^2  0 X^2  0 X^2  0 X^2 X^2  0  0
 0  0  0  0  0  0  0  0  0  0 X^2  0 X^2 X^2  0  0 X^2 X^2  0  0  0  0
 0  0  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0  0

generates a code of length 22 over Z2[X]/(X^3) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+32x^10+117x^12+208x^14+274x^16+416x^18+632x^20+13024x^22+632x^24+416x^26+274x^28+208x^30+117x^32+32x^34+1x^44

The gray image is a linear code over GF(2) with n=88, k=14 and d=20.
This code was found by Heurico 1.16 in 1.21 seconds.