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

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

Homogenous weight enumerator: w(x)=1x^0+130x^68+112x^70+9x^72+1x^80+2x^84+1x^88

The gray image is a code over GF(2) with n=276, k=8 and d=136.
This code was found by Heurico 1.16 in 0.146 seconds.