The generator matrix

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

generates a code of length 24 over Z2[X]/(X^4) who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+19x^18+16x^19+57x^20+48x^21+115x^22+448x^23+656x^24+448x^25+100x^26+48x^27+46x^28+16x^29+20x^30+7x^32+1x^34+1x^36+1x^38

The gray image is a linear code over GF(2) with n=192, k=11 and d=72.
This code was found by Heurico 1.16 in 0.046 seconds.