The generator matrix

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

generates a code of length 67 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 65.

Homogenous weight enumerator: w(x)=1x^0+16x^65+44x^66+128x^67+45x^68+16x^69+2x^70+1x^80+2x^82+1x^84

The gray image is a code over GF(2) with n=268, k=8 and d=130.
This code was found by Heurico 1.16 in 0.13 seconds.