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  1  1  1  1  1  X X^2 X^2  1  X  1  X  X  X  0  X  X  X  0  X  1 X^2
 0  X  0  0  0  0  0  0  0  X X^2+X  X  X X^2+X X^2  0  X X^2+X X^2 X^2  X X^2  0 X^2+X X^2+X X^2  X  0  X  X X^2+X  X  0  0 X^2+X X^2  0  X X^2+X  X  X  0 X^2 X^2+X  X X^2  X X^2
 0  0  X  0  0  0  X X^2+X  X  0  0  0  X  X  0  X X^2  0 X^2+X X^2 X^2+X X^2+X X^2+X  X X^2+X X^2  X  X  0  0  X X^2 X^2  X X^2+X  0 X^2+X  X  X X^2 X^2  X X^2+X X^2 X^2  0  X  0
 0  0  0  X  0  X  X X^2+X  0  X  X X^2  0 X^2 X^2+X  X  X  X X^2+X  0 X^2+X X^2 X^2 X^2  X  0  0 X^2  0 X^2  X X^2  X  0 X^2+X  0  0  0 X^2+X  X  X  X X^2+X  0 X^2  X X^2 X^2
 0  0  0  0  X  X  0 X^2+X  X X^2 X^2+X X^2+X  0 X^2+X X^2 X^2  X X^2  X X^2 X^2+X X^2+X  0 X^2+X X^2  X  0  X X^2+X X^2  X X^2+X  X  X X^2+X  X X^2 X^2 X^2+X  0 X^2+X  0  0  0 X^2 X^2  X X^2
 0  0  0  0  0 X^2  0  0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2  0  0 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0  0 X^2  0 X^2  0  0  0 X^2
 0  0  0  0  0  0 X^2  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 X^2 X^2  0 X^2 X^2  0  0  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2  0  0  0
 0  0  0  0  0  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0  0 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2  0  0  0 X^2 X^2  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+189x^38+8x^39+509x^40+36x^41+861x^42+220x^43+1442x^44+676x^45+1890x^46+1116x^47+2348x^48+1116x^49+2194x^50+660x^51+1406x^52+204x^53+806x^54+44x^55+381x^56+16x^57+185x^58+54x^60+18x^62+1x^64+2x^68+1x^70

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.