The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  X  X  X  1  X  X  1  1  1  X X^2  X X^2
 0 X^3  0  0  0  0  0 X^3  0 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3  0  0 X^3  0 X^3  0 X^3
 0  0 X^3  0  0  0 X^3  0 X^3 X^3 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3
 0  0  0 X^3  0 X^3 X^3 X^3 X^3  0  0 X^3  0 X^3 X^3  0  0 X^3  0 X^3 X^3  0 X^3  0
 0  0  0  0 X^3 X^3  0  0 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3  0  0 X^3  0  0 X^3 X^3  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+12x^21+26x^22+174x^24+16x^25+16x^26+4x^29+6x^30+1x^32

The gray image is a linear code over GF(2) with n=192, k=8 and d=84.
This code was found by Heurico 1.16 in 0.063 seconds.