The generator matrix

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

generates a code of length 37 over Z2[X]/(X^3) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+42x^26+28x^27+148x^28+122x^29+290x^30+352x^31+646x^32+852x^33+1213x^34+1626x^35+1723x^36+2140x^37+1795x^38+1752x^39+1242x^40+880x^41+636x^42+312x^43+282x^44+90x^45+104x^46+24x^47+47x^48+12x^49+13x^50+2x^51+7x^52+3x^54

The gray image is a linear code over GF(2) with n=148, k=14 and d=52.
This code was found by Heurico 1.16 in 8.03 seconds.