The generator matrix

 1  1  1  1  1  1  1  1  1  1  X  1  1  1  X  1  1  1  1 X^2  X  1  X
 0 X^3+X^2  0 X^3+X^2  0 X^3+X^2  0 X^2 X^3  0 X^3+X^2  0 X^3+X^2 X^3+X^2 X^3+X^2 X^2  0 X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^3+X^2
 0  0 X^3  0  0  0  0  0 X^3  0 X^3 X^3  0 X^3 X^3 X^3  0 X^3  0 X^3 X^3 X^3  0
 0  0  0 X^3  0  0  0 X^3  0  0 X^3 X^3 X^3 X^3  0  0 X^3 X^3  0 X^3  0 X^3 X^3
 0  0  0  0 X^3  0  0  0  0 X^3 X^3 X^3  0  0 X^3  0  0  0 X^3 X^3  0 X^3 X^3
 0  0  0  0  0 X^3  0 X^3  0 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3  0  0  0  0 X^3  0
 0  0  0  0  0  0 X^3  0 X^3 X^3  0 X^3 X^3  0  0 X^3  0  0  0 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+50x^18+16x^19+105x^20+64x^21+492x^22+608x^23+492x^24+64x^25+84x^26+16x^27+38x^28+12x^30+3x^32+2x^34+1x^36

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 33.3 seconds.