The generator matrix

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

generates a code of length 34 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+128x^29+353x^30+406x^31+568x^32+394x^33+558x^34+378x^35+476x^36+318x^37+245x^38+138x^39+89x^40+22x^41+12x^42+6x^43+2x^44+2x^45

The gray image is a code over GF(2) with n=136, k=12 and d=58.
This code was found by Heurico 1.11 in 0.141 seconds.