The generator matrix

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

generates a code of length 37 over Z2[X]/(X^3) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+88x^28+12x^29+291x^30+160x^31+743x^32+608x^33+1593x^34+1344x^35+2387x^36+1848x^37+2426x^38+1440x^39+1630x^40+576x^41+734x^42+128x^43+242x^44+28x^45+67x^46+25x^48+9x^50+3x^52+1x^64

The gray image is a linear code over GF(2) with n=148, k=14 and d=56.
This code was found by Heurico 1.16 in 6.27 seconds.