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

generates a code of length 62 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+61x^58+160x^59+306x^60+448x^61+258x^62+544x^63+28x^64+65x^66+128x^67+48x^68+1x^120

The gray image is a code over GF(2) with n=496, k=11 and d=232.
This code was found by Heurico 1.16 in 0.282 seconds.