The generator matrix

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

generates a code of length 39 over Z2[X]/(X^3) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+56x^28+230x^30+8x^31+450x^32+96x^33+966x^34+416x^35+1756x^36+928x^37+2686x^38+1200x^39+2699x^40+928x^41+1756x^42+416x^43+968x^44+96x^45+450x^46+8x^47+189x^48+46x^50+20x^52+10x^54+5x^56

The gray image is a linear code over GF(2) with n=156, k=14 and d=56.
This code was found by Heurico 1.16 in 9 seconds.