The generator matrix

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

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+457x^20+724x^21+2154x^22+2804x^23+3843x^24+3304x^25+1964x^26+776x^27+263x^28+68x^29+10x^30+4x^31+12x^32

The gray image is a linear code over GF(2) with n=192, k=14 and d=80.
This code was found by Heurico 1.16 in 0.938 seconds.