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

generates a code of length 61 over Z2[X]/(X^4) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+178x^56+244x^57+424x^58+432x^59+632x^60+500x^61+560x^62+396x^63+294x^64+152x^65+108x^66+52x^67+67x^68+16x^69+28x^70+11x^72+1x^92

The gray image is a linear code over GF(2) with n=488, k=12 and d=224.
This code was found by Heurico 1.16 in 0.531 seconds.