The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+284x^58+384x^59+325x^60+204x^61+318x^62+248x^63+145x^64+52x^65+64x^66+4x^67+9x^68+4x^71+4x^74+1x^82+1x^90

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 0.188 seconds.