The generator matrix

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

generates a code of length 35 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+46x^34+32x^35+45x^36+2x^38+1x^48+1x^52

The gray image is a code over GF(2) with n=140, k=7 and d=68.
This code was found by Heurico 1.16 in 0.367 seconds.