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

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+260x^32+64x^34+148x^36+34x^40+4x^44+1x^48

The gray image is a code over GF(2) with n=136, k=9 and d=64.
This code was found by Heurico 1.13 in 199 seconds.