The generator matrix

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

generates a code of length 48 over Z2[X]/(X^3) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+140x^38+511x^40+36x^41+871x^42+172x^43+1230x^44+596x^45+2196x^46+1212x^47+2492x^48+1260x^49+2021x^50+644x^51+1449x^52+156x^53+731x^54+20x^55+401x^56+176x^58+53x^60+9x^62+6x^64+1x^72

The gray image is a linear code over GF(2) with n=192, k=14 and d=76.
This code was found by Heurico 1.16 in 13.6 seconds.