The generator matrix

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

generates a code of length 67 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+187x^60+521x^62+605x^64+811x^66+688x^68+690x^70+375x^72+130x^74+37x^76+13x^78+15x^80+11x^82+8x^84+3x^88+1x^96

The gray image is a code over GF(2) with n=268, k=12 and d=120.
This code was found by Heurico 1.16 in 1.5 seconds.