The generator matrix

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

generates a code of length 24 over Z2[X]/(X^4) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+40x^20+8x^21+138x^22+184x^23+314x^24+184x^25+98x^26+8x^27+30x^28+10x^30+6x^32+2x^34+1x^40

The gray image is a linear code over GF(2) with n=192, k=10 and d=80.
This code was found by Heurico 1.16 in 0.015 seconds.