The generator matrix

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

generates a code of length 69 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 61.

Homogenous weight enumerator: w(x)=1x^0+146x^61+1111x^62+2590x^63+4496x^64+7668x^65+10351x^66+13922x^67+16248x^68+17582x^69+16259x^70+14924x^71+10984x^72+7160x^73+3791x^74+2010x^75+1062x^76+482x^77+154x^78+58x^79+39x^80+14x^81+14x^82+2x^84+2x^85+2x^89

The gray image is a code over GF(2) with n=552, k=17 and d=244.
This code was found by Heurico 1.16 in 158 seconds.