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

generates a code of length 51 over Z2[X]/(X^4) who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+74x^45+30x^46+54x^48+64x^49+176x^50+1280x^51+176x^52+44x^53+44x^54+24x^56+64x^57+10x^61+6x^62+1x^96

The gray image is a linear code over GF(2) with n=408, k=11 and d=180.
This code was found by Heurico 1.16 in 35.5 seconds.