The generator matrix

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

generates a code of length 34 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+255x^32+64x^34+156x^36+32x^40+4x^44

The gray image is a code over GF(2) with n=136, k=9 and d=64.
This code was found by Heurico 1.16 in 0.978 seconds.