The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  0  X  1 X^3  1  1  X  1  1  1 X^2  X  X  1  1  X  X
 0  X  0 X^3+X^2+X X^2 X^2+X X^3+X^2  X X^3  0 X^2+X X^2+X  X X^2+X X^2  X X^2 X^3+X X^3+X X^2+X  0 X^2  X X^3+X^2+X X^3  0 X^3 X^3+X^2+X X^3+X^2
 0  0 X^3+X^2  0 X^2  0  0 X^3  0 X^2 X^2 X^2 X^3 X^3+X^2 X^2  0 X^3 X^3+X^2 X^2 X^3+X^2 X^3 X^2  0 X^2  0 X^3 X^2  0 X^3+X^2
 0  0  0 X^3+X^2  0  0 X^3 X^2 X^2 X^2 X^2 X^3 X^3 X^2 X^3+X^2 X^3+X^2 X^2  0 X^2 X^3+X^2  0  0 X^3+X^2 X^3 X^2 X^2  0 X^3+X^2 X^2
 0  0  0  0 X^3 X^3 X^3 X^3  0  0  0 X^3  0  0 X^3  0 X^3  0  0 X^3 X^3  0 X^3  0 X^3 X^3  0  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+57x^24+126x^25+237x^26+520x^27+742x^28+802x^29+741x^30+480x^31+193x^32+82x^33+55x^34+24x^35+14x^36+14x^37+7x^38+1x^40

The gray image is a linear code over GF(2) with n=232, k=12 and d=96.
This code was found by Heurico 1.16 in 0.141 seconds.