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

generates a code of length 61 over Z2[X]/(X^4) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+49x^54+66x^56+256x^60+1280x^61+308x^62+35x^64+26x^70+26x^72+1x^118

The gray image is a linear code over GF(2) with n=488, k=11 and d=216.
This code was found by Heurico 1.16 in 0.39 seconds.