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

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+193x^38+8x^39+454x^40+68x^41+893x^42+224x^43+1497x^44+640x^45+1944x^46+1104x^47+2231x^48+1096x^49+2114x^50+672x^51+1498x^52+224x^53+844x^54+40x^55+412x^56+20x^57+145x^58+45x^60+9x^62+6x^64+1x^70+1x^78

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 31.6 seconds.