The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  X  1  1  X  1  X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  X  X  X  X  X  2  X  X  X  X  0  X  X  2  X 2X  X
 0 2X+2  0  2  0  0  2 2X+2  0  0  2 2X+2  0  0  2 2X+2  0  0  2 2X+2  0  0  2 2X+2  0  0  2 2X+2 2X  0 2X  0  2 2X 2X+2 2X 2X 2X+2 2X  2 2X 2X+2 2X  2 2X 2X+2 2X  2 2X 2X+2 2X  2 2X 2X+2 2X  2 2X 2X 2X+2  2 2X 2X 2X+2  2 2X 2X 2X+2  2  2  2 2X+2  2  2 2X+2 2X+2 2X+2 2X  0  0 2X 2X 2X  2 2X 2X+2  2  2  0
 0  0 2X+2  2  0 2X+2  2  0  0 2X+2  2  0  0 2X+2  2  0 2X  2 2X+2 2X 2X  2 2X+2 2X 2X  2 2X+2 2X  2 2X  2  2 2X+2  2 2X  2 2X 2X+2  2 2X 2X 2X+2  2 2X 2X 2X+2  2 2X  0  2 2X+2  0 2X  2  2  0  0 2X+2  2  0  0 2X+2 2X+2 2X  0 2X+2  2  0  2 2X+2  0  0  2 2X+2  0 2X  2 2X+2  2 2X  0  2  2 2X  0 2X 2X+2  0
 0  0  0 2X  0  0 2X  0 2X 2X  0 2X 2X 2X  0 2X 2X 2X 2X 2X 2X 2X 2X 2X  0  0  0  0  0  0  0  0  0 2X  0 2X  0  0  0  0  0  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X  0  0  0  0 2X 2X 2X 2X  0  0  0  0  0 2X  0 2X  0 2X  0 2X  0  0  0 2X 2X  0 2X 2X 2X 2X 2X 2X
 0  0  0  0 2X 2X 2X 2X 2X 2X  0 2X  0  0 2X  0  0  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X  0  0 2X  0  0 2X  0  0  0  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X  0  0  0  0  0 2X  0 2X 2X  0 2X  0 2X 2X  0  0  0 2X  0 2X  0  0  0  0 2X 2X 2X 2X 2X  0 2X 2X 2X  0  0  0 2X  0  0 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+78x^84+32x^85+196x^86+64x^87+264x^88+160x^89+136x^90+58x^92+20x^94+12x^96+2x^104+1x^128

The gray image is a code over GF(2) with n=704, k=10 and d=336.
This code was found by Heurico 1.16 in 0.797 seconds.