The generator matrix

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

generates a code of length 24 over Z2[X]/(X^4) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+199x^22+210x^23+254x^24+204x^25+103x^26+2x^27+49x^28+2x^34

The gray image is a linear code over GF(2) with n=192, k=10 and d=88.
This code was found by Heurico 1.16 in 0.015 seconds.