The generator matrix

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

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+314x^15+962x^16+2510x^17+4905x^18+9806x^19+14902x^20+21216x^21+21809x^22+21006x^23+15089x^24+10008x^25+5027x^26+2386x^27+717x^28+312x^29+67x^30+24x^31+8x^32+2x^33+1x^36

The gray image is a linear code over GF(2) with n=88, k=17 and d=30.
This code was found by Heurico 1.13 in 50.4 seconds.