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  X  X  2  2  0  0  0  0  X  2  X  X
 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 X+2 X+2  X  X  0  2  X  X  X  2  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  0  0  2  X X+2  X  X X+2  X  2  X X+2 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+19x^32+36x^33+24x^34+24x^35+10x^36+4x^37+6x^38+2x^40+2x^42

The gray image is a code over GF(2) with n=136, k=7 and d=64.
This code was found by Heurico 1.16 in 0.0106 seconds.