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

generates a code of length 87 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+56x^82+112x^83+177x^84+96x^85+215x^86+736x^87+220x^88+96x^89+171x^90+112x^91+46x^92+5x^94+3x^96+1x^98+1x^164

The gray image is a code over GF(2) with n=696, k=11 and d=328.
This code was found by Heurico 1.16 in 0.844 seconds.