The generator matrix

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

generates a code of length 29 over Z2[X]/(X^4) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+40x^24+44x^25+47x^26+224x^27+557x^28+232x^29+557x^30+224x^31+38x^32+44x^33+30x^34+3x^36+3x^38+1x^40+2x^42+1x^50

The gray image is a linear code over GF(2) with n=232, k=11 and d=96.
This code was found by Heurico 1.16 in 0.046 seconds.