The generator matrix

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

generates a code of length 68 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+18x^69+3x^70+4x^71+3x^72+2x^73+1x^78

The gray image is a code over GF(2) with n=272, k=5 and d=138.
This code was found by Heurico 1.16 in 0.133 seconds.