The generator matrix

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

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+499x^56+960x^57+1762x^58+1908x^59+2534x^60+1824x^61+2316x^62+1448x^63+1463x^64+752x^65+492x^66+228x^67+100x^68+48x^69+30x^70+9x^72+6x^74+2x^76+2x^78

The gray image is a code over GF(2) with n=488, k=14 and d=224.
This code was found by Heurico 1.16 in 2.59 seconds.