The generator matrix

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

generates a code of length 47 over Z2[X]/(X^3) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+60x^38+48x^39+113x^40+118x^41+125x^42+252x^43+274x^44+372x^45+474x^46+460x^47+459x^48+384x^49+259x^50+244x^51+120x^52+140x^53+84x^54+20x^55+43x^56+10x^57+15x^58+6x^60+6x^62+8x^64+1x^66

The gray image is a linear code over GF(2) with n=188, k=12 and d=76.
This code was found by Heurico 1.16 in 1.16 seconds.