The generator matrix

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

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+106x^21+267x^22+480x^23+420x^24+422x^25+209x^26+96x^27+26x^28+12x^29+4x^30+4x^31+1x^36

The gray image is a linear code over GF(2) with n=192, k=11 and d=84.
This code was found by Heurico 1.16 in 0.015 seconds.