The generator matrix

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

generates a code of length 36 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+54x^34+52x^35+61x^36+64x^37+2x^38+4x^39+8x^41+8x^42+1x^48+1x^52

The gray image is a code over GF(2) with n=144, k=8 and d=68.
This code was found by Heurico 1.16 in 0.0141 seconds.