The generator matrix

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

generates a code of length 34 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+105x^28+96x^29+342x^30+268x^31+553x^32+380x^33+618x^34+440x^35+552x^36+280x^37+234x^38+60x^39+86x^40+12x^41+54x^42+15x^44

The gray image is a code over GF(2) with n=136, k=12 and d=56.
This code was found by Heurico 1.16 in 0.381 seconds.