The generator matrix

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

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+596x^58+816x^59+692x^60+580x^61+460x^62+300x^63+177x^64+156x^65+110x^66+68x^67+136x^68+2x^72+2x^74

The gray image is a code over GF(2) with n=488, k=12 and d=232.
This code was found by Heurico 1.16 in 101 seconds.