The generator matrix

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

generates a code of length 35 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+82x^28+86x^30+32x^31+260x^32+128x^33+334x^34+192x^35+386x^36+128x^37+194x^38+32x^39+137x^40+26x^42+20x^44+9x^48+1x^56

The gray image is a code over GF(2) with n=140, k=11 and d=56.
This code was found by Heurico 1.16 in 0.169 seconds.