The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+268x^58+434x^59+322x^60+176x^61+284x^62+284x^63+143x^64+48x^65+44x^66+18x^67+12x^68+4x^70+8x^72+1x^80+1x^88

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 0.187 seconds.