The generator matrix

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

generates a code of length 38 over Z2[X]/(X^3) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+99x^24+52x^26+270x^28+156x^30+32x^31+399x^32+224x^33+312x^34+672x^35+476x^36+1120x^37+8683x^38+1120x^39+478x^40+672x^41+516x^42+224x^43+230x^44+32x^45+335x^46+76x^48+136x^50+16x^52+41x^54+3x^56+8x^58+1x^62

The gray image is a linear code over GF(2) with n=152, k=14 and d=48.
This code was found by Heurico 1.16 in 9.02 seconds.