The generator matrix

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

generates a code of length 68 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+224x^64+220x^66+224x^68+176x^70+98x^72+52x^74+12x^76+8x^80+7x^84+1x^88+1x^92

The gray image is a code over GF(2) with n=272, k=10 and d=128.
This code was found by Heurico 1.16 in 0.205 seconds.