The generator matrix

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

generates a code of length 67 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 59.

Homogenous weight enumerator: w(x)=1x^0+254x^59+413x^60+908x^61+906x^62+1186x^63+1083x^64+1482x^65+1251x^66+1666x^67+1258x^68+1422x^69+1030x^70+1254x^71+714x^72+650x^73+364x^74+292x^75+95x^76+78x^77+24x^78+16x^79+18x^80+4x^81+9x^82+4x^83+2x^84

The gray image is a code over GF(2) with n=268, k=14 and d=118.
This code was found by Heurico 1.16 in 17.1 seconds.