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 X^2  0 X^2  X  0 X^2  X  1  X  1  0  1 X^2  1  X  X  X  1 X^2  1  0  X  X  1
 0  X  0  0  0  X X^2+X  X  0 X^2 X^2  X X^2+X  X  X  0 X^2  0  X X^2+X  X X^2  0 X^2+X  0  X  X X^2+X  0  X  0 X^2  X  0  0  0 X^2 X^2  X X^2+X  0  X  X X^2  X X^2+X  X  0
 0  0  X  0  X  X X^2+X  0  0  0  X  X  X  0 X^2 X^2+X X^2 X^2  0 X^2+X  0  X  X X^2+X  X X^2+X  X X^2+X  X X^2+X X^2+X  0 X^2  0  0 X^2  0  X X^2  0 X^2+X X^2 X^2  0 X^2 X^2+X  0  0
 0  0  0  X  X  0 X^2+X  X X^2  X X^2  0  X X^2 X^2+X  X  0  X X^2+X  X X^2 X^2+X  0  0 X^2+X X^2+X X^2  X X^2  0 X^2 X^2+X X^2+X X^2+X  X X^2+X  X X^2+X X^2+X  0  X X^2+X X^2+X X^2  0 X^2+X  X  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  0  0 X^2 X^2  0  0 X^2 X^2 X^2  0  0  0  0  0 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2 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 X^2  0  0 X^2 X^2  0 X^2 X^2  0 X^2  0  0  0 X^2  0 X^2 X^2 X^2 X^2  0  0  0 X^2  0 X^2  0  0  0 X^2  0  0 X^2 X^2 X^2  0
 0  0  0  0  0  0 X^2  0 X^2  0  0 X^2 X^2 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0  0  0  0
 0  0  0  0  0  0  0 X^2  0  0 X^2  0  0  0  0 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2  0 X^2 X^2  0 X^2 X^2  0  0  0  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+43x^38+68x^39+168x^40+200x^41+265x^42+322x^43+510x^44+606x^45+620x^46+840x^47+965x^48+884x^49+529x^50+620x^51+519x^52+296x^53+266x^54+180x^55+120x^56+52x^57+61x^58+18x^59+18x^60+10x^61+6x^62+2x^64+1x^66+1x^68+1x^70

The gray image is a linear code over GF(2) with n=192, k=13 and d=76.
This code was found by Heurico 1.16 in 3.71 seconds.