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

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+189x^56+130x^57+540x^58+364x^59+634x^60+600x^61+594x^62+320x^63+356x^64+84x^65+136x^66+20x^67+58x^68+16x^69+42x^70+9x^72+2x^73+1x^96

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 0.532 seconds.