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

generates a code of length 47 over Z2[X]/(X^3) who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+68x^39+117x^40+148x^41+197x^42+218x^43+318x^44+396x^45+391x^46+388x^47+449x^48+372x^49+324x^50+288x^51+108x^52+100x^53+86x^54+56x^55+23x^56+8x^57+21x^58+6x^59+6x^60+3x^62+2x^64+2x^66

The gray image is a linear code over GF(2) with n=188, k=12 and d=78.
This code was found by Heurico 1.16 in 18.5 seconds.