The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1  0  1
 0  X  0  0  0  0  0  0 X^2 X^2  X  X X^2+X  X X^2+X X^2+X  0 X^2 X^2 X^2+X  0  0
 0  0  X  0  0  0  0  0  0  0  0 X^2 X^2 X^2+X X^2+X X^2+X X^2+X X^2+X X^2+X  X X^2 X^2
 0  0  0  X  0  0 X^2 X^2+X  X  X  X  X X^2 X^2+X X^2  X X^2 X^2 X^2+X  X  0  X
 0  0  0  0  X  0 X^2+X X^2+X  X X^2  0  0  X  X X^2+X  X X^2  X X^2  0  X X^2+X
 0  0  0  0  0  X  X X^2 X^2+X  X X^2 X^2+X  X  0  0 X^2+X X^2+X  0  X X^2+X X^2  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+52x^15+142x^16+214x^17+269x^18+340x^19+597x^20+1422x^21+2045x^22+1460x^23+682x^24+370x^25+223x^26+188x^27+111x^28+42x^29+23x^30+8x^31+2x^32+1x^40

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 1.01 seconds.