The generator matrix

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

generates a code of length 38 over Z2[X]/(X^3) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+46x^26+16x^27+141x^28+44x^29+196x^30+160x^31+428x^32+348x^33+1246x^34+640x^35+2460x^36+856x^37+3182x^38+800x^39+2568x^40+664x^41+1239x^42+368x^43+437x^44+124x^45+181x^46+64x^47+89x^48+12x^49+44x^50+18x^52+8x^54+2x^56+1x^58+1x^62

The gray image is a linear code over GF(2) with n=152, k=14 and d=52.
This code was found by Heurico 1.16 in 8.6 seconds.