The generator matrix

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

generates a code of length 67 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+62x^55+249x^56+788x^57+1356x^58+2274x^59+3348x^60+4626x^61+6224x^62+7888x^63+9488x^64+10834x^65+11696x^66+12484x^67+12248x^68+10882x^69+10264x^70+8312x^71+6091x^72+4492x^73+3056x^74+1924x^75+1064x^76+698x^77+336x^78+194x^79+83x^80+62x^81+28x^82+14x^83+4x^84+2x^85

The gray image is a code over GF(2) with n=268, k=17 and d=110.
This code was found by Heurico 1.13 in 225 seconds.