The generator matrix

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

generates a code of length 89 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+75x^84+120x^85+134x^86+44x^87+142x^88+88x^89+92x^90+12x^91+119x^92+104x^93+54x^94+4x^95+6x^96+8x^97+8x^98+4x^99+4x^100+2x^104+1x^120+2x^124

The gray image is a code over GF(2) with n=356, k=10 and d=168.
This code was found by Heurico 1.16 in 0.468 seconds.