The generator matrix

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

generates a code of length 35 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+82x^27+151x^28+190x^29+302x^30+404x^31+486x^32+786x^33+1162x^34+1134x^35+1013x^36+894x^37+557x^38+354x^39+271x^40+150x^41+114x^42+72x^43+28x^44+28x^45+8x^46+2x^47+2x^48+1x^54

The gray image is a code over GF(2) with n=140, k=13 and d=54.
This code was found by Heurico 1.16 in 2.53 seconds.