The generator matrix

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

generates a code of length 67 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+111x^58+236x^59+493x^60+618x^61+899x^62+1082x^63+1179x^64+1466x^65+1459x^66+1506x^67+1453x^68+1392x^69+1194x^70+1056x^71+801x^72+562x^73+375x^74+184x^75+139x^76+52x^77+49x^78+30x^79+26x^80+4x^81+7x^82+2x^83+3x^84+2x^85+2x^86+1x^88

The gray image is a code over GF(2) with n=268, k=14 and d=116.
This code was found by Heurico 1.16 in 12.8 seconds.