The generator matrix

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

generates a code of length 45 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+47x^44+32x^45+40x^46+5x^48+2x^56+1x^60

The gray image is a code over GF(2) with n=180, k=7 and d=88.
This code was found by Heurico 1.16 in 0.0289 seconds.