The generator matrix

 1  1  1  1  1  1  1  1  1  X  1  0  1  1  1  1  1  1  1  1 X^3+X^2  X X^3  X
 0  X  0 X^2+X X^2 X^3+X^2+X X^3+X^2  X  0 X^3+X^2+X X^3+X^2+X  X X^2  X X^3 X^3+X^2 X^2+X X^3+X  0 X^2+X  X X^3 X^2 X^3+X^2
 0  0 X^3+X^2  0 X^2 X^2 X^3 X^2  0 X^3+X^2 X^2 X^3 X^2 X^3+X^2 X^2  0  0 X^3 X^3 X^2 X^3 X^3+X^2 X^2  0
 0  0  0 X^3  0  0 X^3  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3  0 X^3 X^3 X^3 X^3
 0  0  0  0 X^3  0  0 X^3 X^3  0  0 X^3 X^3 X^3  0 X^3 X^3 X^3  0 X^3 X^3 X^3  0  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+87x^20+60x^21+249x^22+392x^23+499x^24+400x^25+242x^26+24x^27+42x^28+20x^29+21x^30+10x^32+1x^36

The gray image is a linear code over GF(2) with n=192, k=11 and d=80.
This code was found by Heurico 1.16 in 0.031 seconds.