The generator matrix

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

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+176x^21+696x^22+724x^23+1114x^24+586x^25+479x^26+192x^27+101x^28+18x^29+9x^30

The gray image is a linear code over GF(2) with n=192, k=12 and d=84.
This code was found by Heurico 1.16 in 0.047 seconds.