The generator matrix

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

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+94x^28+234x^29+289x^30+424x^31+637x^32+900x^33+1192x^34+1486x^35+1825x^36+2120x^37+1924x^38+1468x^39+1282x^40+932x^41+610x^42+416x^43+231x^44+158x^45+75x^46+44x^47+24x^48+8x^49+6x^50+2x^51+1x^52+1x^60

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 9.81 seconds.