The generator matrix

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

generates a code of length 23 over Z2[X]/(X^4) who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+27x^18+54x^19+100x^20+210x^21+396x^22+536x^23+377x^24+156x^25+83x^26+46x^27+30x^28+18x^29+6x^30+4x^31+4x^32

The gray image is a linear code over GF(2) with n=184, k=11 and d=72.
This code was found by Heurico 1.16 in 0.031 seconds.