The generator matrix

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

generates a code of length 36 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+235x^28+32x^29+450x^30+304x^31+1237x^32+960x^33+1946x^34+1744x^35+2464x^36+1824x^37+2020x^38+976x^39+1261x^40+256x^41+420x^42+48x^43+147x^44+26x^46+28x^48+2x^50+2x^52+1x^56

The gray image is a code over GF(2) with n=144, k=14 and d=56.
This code was found by Heurico 1.16 in 22.3 seconds.