The generator matrix

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

generates a code of length 53 over Z2[X]/(X^4) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+72x^48+274x^49+266x^50+616x^51+446x^52+794x^53+432x^54+634x^55+237x^56+210x^57+64x^58+26x^59+11x^60+2x^61+2x^63+4x^66+2x^67+1x^70+1x^76+1x^78

The gray image is a linear code over GF(2) with n=424, k=12 and d=192.
This code was found by Heurico 1.16 in 0.282 seconds.