The generator matrix

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

generates a code of length 29 over Z2[X]/(X^3) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+102x^20+90x^22+96x^23+534x^24+704x^25+1056x^26+1952x^27+2375x^28+2688x^29+2116x^30+1952x^31+1335x^32+704x^33+304x^34+96x^35+225x^36+18x^38+34x^40+1x^44+1x^52

The gray image is a linear code over GF(2) with n=116, k=14 and d=40.
This code was found by Heurico 1.16 in 3.76 seconds.