The generator matrix

 1  0  0  1  1  1  2  0  0  1  1  2  1  1  X X+2  1  0  1  1  1  2  1  0  1  1  2  1  0  X X+2 X+2  0  X  0  X  X  X  X  X  X  X  X  1  1  1  1  1  1  1  1  1  2  1  1  1  1  X  X  1  1  1  1  1  1  1  1  1
 0  1  0  0  3  3  1 X+2  1  2  1  1  2  1  X  2  2  1  3  1  0  1  2  1  1  0  1  3 X+2 X+2  0  X  X  0  X  1  1  1  1  1  1  1  1  X X+2 X+1 X+3 X+2 X+3 X+2  X X+1  0  X X+1 X+2  X X+2  2 X+3 X+3 X+1  X X+2 X+1 X+3 X+3 X+1
 0  0  1 X+1 X+3  2 X+3  1 X+2 X+2  X  3  3  1  1  1 X+3  2  3  0  X  3  2  X X+1  1 X+3 X+2  1  1  1  1  1  1  1  X  1  3  X  2  2 X+3 X+1  X  3  0 X+3 X+3  1  X  3 X+3  1  2  1 X+3  0  1  1  0 X+2 X+2  0 X+1  0  1  3 X+1
 0  0  0  2  2  0  2  2  2  2  2  0  0  0  0  2  0  2  2  2  0  2  2  0  0  2  0  0  0  2  0  2  2  0  0  0  2  0  2  0  2  0  2  0  2  2  0  2  2  2  0  2  2  0  0  0  2  0  2  0  2  0  0  2  0  0  0  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+79x^64+128x^65+270x^66+128x^67+91x^68+32x^69+92x^70+32x^71+32x^72+32x^73+42x^74+32x^75+9x^76+4x^78+18x^80+2x^84

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 0.182 seconds.