The generator matrix

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

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+424x^18+2196x^19+6509x^20+14424x^21+26066x^22+31544x^23+26269x^24+14976x^25+6254x^26+1812x^27+495x^28+72x^29+22x^30+6x^32+2x^34

The gray image is a linear code over GF(2) with n=184, k=17 and d=72.
This code was found by Heurico 1.16 in 35.4 seconds.