The generator matrix

 1  0  0  0  1  1  1 X^2  1 X^2  X  1  1  1  1 X^2  X  1  X  0 X^2  1
 0  1  0  0  0  1  1  1 X+1  X  1 X^2+X  X X^2+1  1  1 X^2 X^2  X  0  1 X^2
 0  0  1  0  1  1  X X+1  0  1 X^2 X^2+1  X  1  0 X+1  1  0  1  1 X^2+1 X^2
 0  0  0  1  1  0 X+1  1 X^2 X^2+1  1  X  1 X+1 X^2  X X^2 X^2+X+1  1 X^2+X+1 X+1 X^2
 0  0  0  0  X X^2  0 X^2 X^2  X  0  0 X^2+X  X  X  0  X X^2 X^2+X X^2  X 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+71x^16+352x^17+780x^18+1160x^19+2001x^20+2282x^21+2979x^22+2392x^23+2110x^24+1196x^25+634x^26+272x^27+105x^28+26x^29+23x^30

The gray image is a linear code over GF(2) with n=88, k=14 and d=32.
This code was found by Heurico 1.13 in 0.86 seconds.