The generator matrix

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

generates a code of length 39 over Z2[X]/(X^3) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+144x^24+260x^28+91x^30+505x^32+224x^33+126x^34+224x^35+476x^36+1120x^37+398x^38+9312x^39+440x^40+672x^41+534x^42+672x^43+156x^44+32x^45+532x^46+32x^47+62x^48+218x^50+4x^52+130x^54+18x^58+1x^62

The gray image is a linear code over GF(2) with n=156, k=14 and d=48.
This code was found by Heurico 1.16 in 9.06 seconds.