The generator matrix

 1  0  0  1  1  1  X X+2  0  2  1  1  1  1  1 X+2  2  1  1  1  X  2  1  2  1  2 X+2  X  1  X  X  1  0  1
 0  1  0  X  1 X+3  1  1  1  X  2  X X+1  3  2  1  1  2  X  3  1  1 X+3  1 X+3  X  1 X+2  0  1  X  3  1  0
 0  0  1  1 X+3 X+2  1 X+1 X+2  1  X X+3 X+1  0  1  0  1 X+3  X X+1  X  X X+2 X+3  3  1  X  1 X+2 X+3  1  2  0  0
 0  0  0  2  0  0  0  2  2  2  0  2  0  0  2  0  0  2  2  2  0  2  0  0  2  0  2  2  2  0  2  0  2  0
 0  0  0  0  2  0  0  0  0  0  2  2  2  2  0  0  2  2  0  2  2  0  0  2  0  0  2  2  2  0  2  0  0  0
 0  0  0  0  0  2  0  2  2  2  2  2  2  2  2  2  0  0  2  2  2  0  0  2  0  2  2  0  2  2  2  2  0  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+48x^28+196x^29+230x^30+442x^31+382x^32+574x^33+499x^34+484x^35+359x^36+374x^37+211x^38+194x^39+37x^40+36x^41+17x^42+5x^44+2x^45+3x^46+2x^49

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 0.307 seconds.