The generator matrix

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

generates a code of length 61 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+573x^54+1924x^55+4273x^56+7226x^57+10970x^58+14004x^59+17369x^60+17782x^61+18660x^62+14088x^63+10569x^64+7136x^65+3746x^66+1540x^67+826x^68+264x^69+65x^70+28x^71+17x^72+6x^73+2x^77+2x^78+1x^92

The gray image is a code over GF(2) with n=488, k=17 and d=216.
This code was found by Heurico 1.16 in 125 seconds.