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

generates a code of length 61 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+44x^56+110x^57+130x^58+90x^59+418x^60+532x^61+397x^62+68x^63+99x^64+62x^65+46x^66+18x^67+14x^68+16x^69+2x^70+1x^110

The gray image is a code over GF(2) with n=488, k=11 and d=224.
This code was found by Heurico 1.16 in 0.344 seconds.