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

generates a code of length 61 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 59.

Homogenous weight enumerator: w(x)=1x^0+124x^59+106x^60+116x^61+60x^62+36x^63+19x^64+44x^65+2x^66+2x^68+2x^74

The gray image is a code over GF(2) with n=488, k=9 and d=236.
This code was found by Heurico 1.16 in 1.44 seconds.