The generator matrix

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

generates a code of length 67 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+124x^62+128x^63+448x^64+120x^65+362x^66+92x^67+212x^68+56x^69+158x^70+60x^71+89x^72+28x^73+58x^74+24x^75+51x^76+4x^77+18x^78+14x^80+1x^84

The gray image is a code over GF(2) with n=268, k=11 and d=124.
This code was found by Heurico 1.11 in 0.203 seconds.