The generator matrix

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

generates a code of length 87 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+26x^86+56x^87+27x^88+3x^90+8x^91+4x^92+2x^94+1x^98

The gray image is a code over GF(2) with n=348, k=7 and d=172.
This code was found by Heurico 1.16 in 0.351 seconds.