The generator matrix

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

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+292x^48+860x^49+1724x^50+2010x^51+2572x^52+2264x^53+2225x^54+1594x^55+1361x^56+756x^57+440x^58+166x^59+38x^60+24x^61+41x^62+6x^63+8x^64+2x^66

The gray image is a linear code over GF(2) with n=424, k=14 and d=192.
This code was found by Heurico 1.16 in 2.83 seconds.