The generator matrix

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

generates a code of length 41 over Z2[X]/(X^3) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+178x^28+482x^32+804x^36+640x^38+2169x^40+8192x^41+1280x^42+1584x^44+128x^46+612x^48+236x^52+62x^56+14x^60+1x^64+1x^72

The gray image is a linear code over GF(2) with n=164, k=14 and d=56.
This code was found by Heurico 1.16 in 11.8 seconds.