The generator matrix

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

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+47x^20+52x^22+64x^23+707x^24+64x^25+48x^26+24x^28+12x^30+4x^32+1x^44

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.