The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+192x^84+696x^85+736x^86+614x^87+374x^88+428x^89+252x^90+206x^91+166x^92+128x^93+120x^94+104x^95+25x^96+32x^97+17x^98+1x^100+3x^102+1x^104

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 0.531 seconds.