The generator matrix

 1  0  0  1  1  1 X+2  1  2  1  1  X  1  0  1  1  2 X+2 X+2  1  1  2  1 X+2  1  2  1  1 X+2  1  X  1  1  1  1  1  0  2  1  0  1  1  1  1  1  1  X  1  2  1  1 X+2  1  0  2  1  1  1  0  1 X+2  1  2  X  1  1  1
 0  1  0  0  1 X+3  1  3  1  X  2  X  3  1  2 X+3  0  1  1 X+1 X+2  1  3  2  X  1  3  2  X  0  1  1  0  X X+1 X+3  1  1  3  1  0  X  3  0  0  1  1  X  1 X+2 X+3  1  3  1  2 X+1 X+1  0 X+2 X+3  1  3  1  2  X  2  X
 0  0  1  1  1  0  1  X X+1 X+3  X  1 X+3  X X+2  X  1 X+1  0  1 X+1  X X+3  1  0  3  2  1  1  3 X+1  1  X  3  1  0  0  1  3 X+3 X+2  0  3  1  3  2 X+2  3 X+2 X+3  1  3 X+3  0  1  1  2 X+1  1  X  2  1 X+1  1  X  X  1
 0  0  0  X  0  0  2  0  2  X  0  0  0  0 X+2 X+2  X X+2 X+2 X+2  2 X+2 X+2  X  X  X  0  X  X  2  2  2  2  0  X X+2  2 X+2  2  X X+2 X+2 X+2  0  X X+2  0  0  2 X+2  0  2 X+2  X  0  0  2  0  2 X+2  X  X X+2 X+2 X+2  X  X
 0  0  0  0  X X+2 X+2 X+2  X  0  0  2  X X+2  2 X+2  2  X  X  X  0  X X+2  2  0 X+2  0  X  X X+2  2  0  X X+2  2  2  X  2  2  0  X X+2  2  X  X  0  2  0  0  0  X  0  2  2 X+2  0 X+2  2  X  X  0  2  0 X+2 X+2 X+2  X
 0  0  0  0  0  2  0  0  2  2  2  2  2  2  2  0  2  2  0  2  0  2  0  0  0  2  2  2  0  0  2  0  0  2  0  0  0  0  2  2  2  0  2  2  0  2  0  2  2  0  0  0  0  2  2  2  2  2  2  0  0  0  0  0  0  0  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+80x^58+290x^59+406x^60+744x^61+825x^62+1230x^63+1005x^64+1564x^65+1282x^66+1628x^67+1352x^68+1566x^69+994x^70+1224x^71+752x^72+650x^73+284x^74+208x^75+104x^76+74x^77+45x^78+24x^79+24x^80+10x^81+10x^82+2x^83+2x^84+2x^87+2x^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 13.5 seconds.