The generator matrix

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

generates a code of length 88 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+164x^84+774x^85+532x^86+806x^87+398x^88+344x^89+240x^90+266x^91+108x^92+206x^93+81x^94+116x^95+32x^96+16x^97+8x^98+2x^102+1x^108+1x^114

The gray image is a code over GF(2) with n=704, k=12 and d=336.
This code was found by Heurico 1.16 in 0.484 seconds.