The generator matrix

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

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+249x^22+128x^23+283x^24+128x^25+224x^26+3x^28+6x^30+1x^36+1x^38

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 2.06 seconds.