The generator matrix

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

generates a code of length 32 over Z2[X]/(X^3) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+69x^22+36x^23+168x^24+158x^25+337x^26+478x^27+1053x^28+1256x^29+1116x^30+2144x^31+2672x^32+2164x^33+1162x^34+1316x^35+1082x^36+488x^37+325x^38+108x^39+118x^40+30x^41+53x^42+14x^43+25x^44+10x^46+1x^48

The gray image is a linear code over GF(2) with n=128, k=14 and d=44.
This code was found by Heurico 1.16 in 6.31 seconds.