The generator matrix

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

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+166x^28+32x^29+256x^30+160x^31+807x^32+320x^33+640x^34+320x^35+792x^36+160x^37+256x^38+32x^39+128x^40+18x^44+8x^48

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 96.3 seconds.