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

generates a code of length 88 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 83.

Homogenous weight enumerator: w(x)=1x^0+80x^83+62x^84+138x^85+166x^86+364x^87+449x^88+358x^89+148x^90+128x^91+62x^92+78x^93+6x^94+4x^95+1x^96+2x^97+1x^168

The gray image is a code over GF(2) with n=704, k=11 and d=332.
This code was found by Heurico 1.16 in 0.937 seconds.