The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+138x^61+987x^62+2626x^63+4688x^64+7594x^65+10501x^66+13576x^67+16546x^68+17074x^69+17431x^70+14150x^71+10692x^72+7216x^73+4069x^74+2112x^75+858x^76+444x^77+224x^78+76x^79+43x^80+10x^81+2x^82+4x^83+4x^84+4x^85+2x^86

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 155 seconds.