The generator matrix

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

generates a code of length 61 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+398x^53+1555x^54+4376x^55+7761x^56+13294x^57+19281x^58+29502x^59+35809x^60+38322x^61+34893x^62+29870x^63+20704x^64+13614x^65+6861x^66+3508x^67+1401x^68+592x^69+220x^70+128x^71+18x^72+20x^73+6x^74+6x^75+2x^76+2x^79

The gray image is a code over GF(2) with n=488, k=18 and d=212.
This code was found by Heurico 1.16 in 600 seconds.