The generator matrix

 1  0  0  0  0  1  1  1  X  1  1  1 X^2  0  0  X  1 X^2  0  X X^2  1
 0  1  0  0  0  0 X^2  0 X^2  1 X+1 X^2+X+1 X^2+X  1  1  1 X+1  1 X^2+X  1  1  0
 0  0  1  0  0  0  1  1  1 X^2+1 X+1  X  1 X^2+X+1 X+1 X^2 X^2+X X^2+X X^2+X X^2 X^2+X+1  0
 0  0  0  1  0  1  1  X X^2+X+1 X^2 X^2+X  0 X^2+1 X^2+X X^2+1 X^2+1 X+1 X^2+1  1  0 X+1  0
 0  0  0  0  1  1  X X+1  1  0  1 X+1 X^2+X X^2+X+1  1 X^2 X^2+X+1 X+1 X^2+X+1 X+1 X^2+1  0
 0  0  0  0  0 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0  0 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 15.

Homogenous weight enumerator: w(x)=1x^0+106x^15+466x^16+1334x^17+2634x^18+4836x^19+7403x^20+9940x^21+11585x^22+10368x^23+7791x^24+4920x^25+2433x^26+1068x^27+401x^28+188x^29+51x^30+6x^31+2x^32+2x^33+1x^34

The gray image is a linear code over GF(2) with n=88, k=16 and d=30.
This code was found by Heurico 1.13 in 10.3 seconds.