The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1  1  X  1 X^2  1 X^2  X  1  1
 0 X^3+X^2  0 X^3+X^2  0 X^3+X^2  0 X^2 X^3 X^3+X^2  0  0 X^3+X^2 X^3+X^2 X^2  0 X^3 X^3+X^2 X^2 X^3  0 X^3+X^2 X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^2  0
 0  0 X^3  0  0  0  0  0 X^3  0  0 X^3  0 X^3  0 X^3  0 X^3 X^3 X^3  0  0 X^3  0  0 X^3  0 X^3 X^3
 0  0  0 X^3  0  0  0 X^3  0  0  0  0 X^3 X^3 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0  0  0 X^3 X^3  0  0
 0  0  0  0 X^3  0  0  0  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0  0 X^3  0 X^3 X^3  0  0  0
 0  0  0  0  0 X^3  0 X^3  0 X^3 X^3 X^3  0 X^3  0 X^3  0  0  0  0  0 X^3 X^3 X^3  0  0  0 X^3 X^3
 0  0  0  0  0  0 X^3  0 X^3  0 X^3  0 X^3  0 X^3 X^3 X^3 X^3  0 X^3 X^3  0 X^3  0  0  0  0 X^3  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+90x^24+112x^26+192x^27+193x^28+896x^29+160x^30+192x^31+144x^32+48x^34+14x^36+4x^40+1x^44+1x^48

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 0.063 seconds.