The generator matrix

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

generates a code of length 49 over Z2[X]/(X^4) who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+136x^45+401x^46+968x^47+426x^48+508x^49+355x^50+732x^51+256x^52+148x^53+74x^54+60x^55+20x^56+8x^57+1x^62+1x^64+1x^66

The gray image is a linear code over GF(2) with n=392, k=12 and d=180.
This code was found by Heurico 1.16 in 0.219 seconds.