The generator matrix

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

generates a code of length 61 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+316x^58+328x^59+347x^60+292x^61+257x^62+212x^63+127x^64+44x^65+65x^66+20x^67+28x^68+5x^70+4x^74+1x^76+1x^82

The gray image is a code over GF(2) with n=488, k=11 and d=232.
This code was found by Heurico 1.16 in 0.281 seconds.