The generator matrix

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

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+110x^18+1164x^19+3225x^20+7580x^21+12847x^22+15538x^23+13007x^24+7886x^25+2948x^26+940x^27+239x^28+36x^29+7x^30+6x^31+2x^33

The gray image is a linear code over GF(2) with n=184, k=16 and d=72.
This code was found by Heurico 1.16 in 12.7 seconds.