The generator matrix

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

generates a code of length 34 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+144x^29+315x^30+446x^31+454x^32+560x^33+483x^34+478x^35+346x^36+344x^37+221x^38+162x^39+87x^40+40x^41+13x^42+2x^43

The gray image is a code over GF(2) with n=136, k=12 and d=58.
This code was found by Heurico 1.16 in 0.287 seconds.