The generator matrix

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

generates a code of length 22 over Z2[X]/(X^3) who´s minimum homogenous weight is 15.

Homogenous weight enumerator: w(x)=1x^0+36x^15+138x^16+584x^18+592x^19+1312x^20+1920x^22+1272x^23+1576x^24+560x^26+144x^27+32x^28+4x^31+13x^32+8x^34

The gray image is a linear code over GF(2) with n=88, k=13 and d=30.
This code was found by Heurico 1.16 in 58.6 seconds.