The generator matrix

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

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+56x^34+64x^35+12x^36+64x^37+55x^38+2x^40+1x^48+1x^54

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 0.0144 seconds.