The generator matrix

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

generates a code of length 22 over Z2[X]/(X^3) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+314x^16+568x^17+1438x^18+2376x^19+3687x^20+5232x^21+5362x^22+5296x^23+3990x^24+2360x^25+1298x^26+520x^27+256x^28+32x^29+30x^30+7x^32+1x^36

The gray image is a linear code over GF(2) with n=88, k=15 and d=32.
This code was found by Heurico 1.16 in 13.1 seconds.