The generator matrix

 1  0  0  0  1  1  1  1 X^3+X  1 X^3+X^2 X^2  1 X^2  1  1 X^2+X  1  1  1 X^3+X^2  X X^3  X  1  1 X^3+X  1  1 X^3+X  1  0 X^3  1 X^3+X^2  X  1  1  1  1 X^2+X  1  1  1  1 X^3+X X^3+X X^3+X^2+X  1
 0  1  0  0  0 X^3 X^2+1 X^3+X+1  1 X^3+1  1 X^3+X^2+X X+1  1 X^2+X X^3  1 X^3+X^2+X+1  X X^2+X+1  1  1  1  X X^2+X X^2+1 X^2 X^3+X^2+X+1  0 X^3+X X^2 X^3+X^2+X  1 X^3+X^2+X X^3+X^2  1 X^3+X^2  1 X^3+X^2+X+1 X^2  0 X^3+X+1 X^3+X^2+X+1 X^3  0 X^2+X X^3+X^2+X  0 X^2
 0  0  1  0  1 X^3+X^2+X X^2  X  X  1 X^2+1  1 X^2+1 X^3+X^2+X+1 X+1 X+1 X^3+X^2+X+1 X^3  0 X^3+X X^3+X+1 X^3+X^2+X X^2+X  1 X^3 X^2+X+1  1 X^3+1 X^2+X X^3+X^2 X^3+X+1  1 X^3+X^2+X+1 X+1  1  0  1 X^2+X X^3+X+1 X^2  X  0 X^3+1 X^3+X^2+X+1 X^3  1  1 X^2+X  0
 0  0  0  1  1 X+1 X^2+X+1 X^3 X+1  X X^2+1 X^3+X+1 X^3+X+1 X^3+X X^2+X X^3+X^2+X+1 X^3+X^2 X^3+X+1 X^3  X X^3+X+1  X X^3+X^2+X+1 X+1 X^3+1 X^3+X^2+X+1 X^3+X^2+X X^3 X^3+X^2  1 X^2+X X^2+1 X^2+1 X^2 X+1 X^3+X X^3+X^2 X^3 X^3+X^2+1  X  1 X^3+X X^2+X X^3+X^2+1 X^3+X X^2+1  0  1  X
 0  0  0  0 X^3  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0 X^3  0 X^3 X^3 X^3  0 X^3  0  0 X^3  0  0

generates a code of length 49 over Z2[X]/(X^4) who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+190x^42+1154x^43+3232x^44+6006x^45+10130x^46+14916x^47+19326x^48+20662x^49+19702x^50+15506x^51+10450x^52+5656x^53+2551x^54+960x^55+391x^56+136x^57+62x^58+24x^59+8x^60+2x^61+5x^62+2x^65

The gray image is a linear code over GF(2) with n=392, k=17 and d=168.
This code was found by Heurico 1.16 in 99.8 seconds.