The generator matrix

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

generates a code of length 24 over Z2[X]/(X^4) who´s minimum homogenous weight is 21.

Homogenous weight enumerator: w(x)=1x^0+66x^21+111x^22+302x^23+117x^24+284x^25+73x^26+28x^27+10x^28+18x^29+7x^30+6x^31+1x^42

The gray image is a linear code over GF(2) with n=192, k=10 and d=84.
This code was found by Heurico 1.16 in 0.016 seconds.