The generator matrix

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

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+146x^62+134x^64+270x^66+208x^68+154x^70+39x^72+58x^74+12x^78+1x^80+1x^120

The gray image is a code over GF(2) with n=268, k=10 and d=124.
This code was found by Heurico 1.16 in 61.4 seconds.