The generator matrix

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

generates a code of length 67 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+60x^64+120x^65+90x^66+60x^67+49x^68+48x^69+26x^70+12x^71+17x^72+16x^73+4x^74+6x^76+2x^80+1x^84

The gray image is a code over GF(2) with n=268, k=9 and d=128.
This code was found by Heurico 1.16 in 0.0961 seconds.