The generator matrix

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

generates a code of length 34 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+122x^28+88x^29+382x^30+244x^31+496x^32+408x^33+614x^34+488x^35+487x^36+232x^37+284x^38+68x^39+127x^40+8x^41+30x^42+15x^44+2x^46

The gray image is a code over GF(2) with n=136, k=12 and d=56.
This code was found by Heurico 1.16 in 0.376 seconds.