The generator matrix

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

generates a code of length 69 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+148x^62+1482x^63+2446x^64+4108x^65+5165x^66+7656x^67+7197x^68+9220x^69+7683x^70+7650x^71+4810x^72+4112x^73+1936x^74+1064x^75+477x^76+228x^77+67x^78+48x^79+5x^80+12x^81+9x^82+4x^83+8x^84

The gray image is a code over GF(2) with n=552, k=16 and d=248.
This code was found by Heurico 1.16 in 37.6 seconds.