The generator matrix

 1  0  0  0  1  1  1 X^2+X  1  1  1  1 X^2 X^2+X  0  1  1  1 X^2  1 X^3+X^2+X  0  1
 0  1  0  0  X X^3+1 X^2+X+1  1 X^2+X X^3+1 X^2+1 X^2  1  1  X  1  0 X^2  1 X^2  1  1 X^3+X
 0  0  1  0 X+1  1  X X+1 X^3+X^2+1 X^2+1 X^2+X X^2 X^2 X^2+X+1  1 X^2 X^3+X+1 X^2  X X^2+X+1  X X^3+X^2+X  X
 0  0  0  1  1 X^2 X+1 X+1 X^2+X X+1 X^2+X X^2+1  1 X^3 X^2+1 X^3+X^2+X X^3 X^2 X^3+X^2+X+1  X X^3+X X^3+X^2+1 X^2+X+1
 0  0  0  0 X^2  0  0  0  0 X^3 X^3 X^3 X^3+X^2 X^2 X^3+X^2 X^2 X^3+X^2 X^2 X^3  0 X^3+X^2 X^3+X^2  0

generates a code of length 23 over Z2[X]/(X^4) who´s minimum homogenous weight is 17.

Homogenous weight enumerator: w(x)=1x^0+148x^17+1085x^18+4124x^19+12732x^20+28174x^21+51693x^22+64970x^23+53456x^24+28672x^25+11943x^26+3696x^27+1132x^28+254x^29+47x^30+10x^31+7x^32

The gray image is a linear code over GF(2) with n=184, k=18 and d=68.
This code was found by Heurico 1.16 in 132 seconds.