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  X  X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  X  X  1
 0 2X+2  0 2X+2  0 2X+2  0 2X+2  0 2X+2  0 2X+2  0 2X+2  0 2X+2  0 2X+2  0 2X+2  0 2X+2  0 2X+2 2X  2 2X  2 2X  2 2X  2  0 2X+2 2X  2 2X  2 2X  2  0 2X+2 2X  2 2X  2 2X  2  0  2 2X 2X+2 2X  2 2X  2  0 2X+2 2X  2 2X  2 2X  2 2X+2 2X+2  0 2X+2  0 2X+2  0 2X+2  0 2X+2 2X 2X+2  2 2X+2  2  0 2X 2X 2X+2 2X+2 2X+2 2X+2  0
 0  0 2X  0  0  0 2X  0  0  0  0  0 2X  0 2X  0  0 2X  0 2X  0 2X  0 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X  0  0  0  0 2X 2X 2X 2X  0  0  0  0 2X 2X 2X 2X  0  0  0  0 2X 2X 2X 2X  0  0  0  0  0  0  0  0  0  0 2X 2X 2X 2X  0 2X 2X 2X 2X  0  0  0  0  0  0 2X  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 2X  0 2X  0 2X  0  0 2X 2X 2X  0  0 2X  0  0 2X 2X 2X  0  0 2X 2X  0  0 2X 2X  0  0 2X  0  0 2X 2X 2X  0  0  0  0  0  0 2X 2X 2X  0 2X  0 2X 2X  0  0 2X  0 2X  0  0 2X  0 2X  0
 0  0  0  0 2X  0 2X  0  0 2X 2X 2X 2X 2X  0 2X 2X  0 2X  0  0 2X  0 2X 2X  0 2X  0  0 2X  0 2X  0 2X  0 2X  0 2X  0 2X  0 2X  0 2X 2X  0 2X  0 2X  0 2X  0 2X 2X 2X 2X 2X  0 2X  0  0  0  0  0  0  0  0 2X 2X  0  0 2X  0 2X 2X 2X  0  0 2X 2X  0  0  0 2X 2X  0  0
 0  0  0  0  0 2X  0 2X 2X 2X 2X  0 2X  0 2X 2X  0  0 2X 2X 2X 2X  0  0  0  0 2X 2X 2X 2X  0  0  0  0  0  0  0  0  0  0 2X 2X 2X 2X 2X 2X  0  0 2X 2X 2X  0  0 2X 2X 2X  0 2X  0  0 2X  0 2X 2X  0 2X  0 2X  0  0  0  0 2X 2X 2X 2X  0 2X  0 2X 2X 2X  0  0 2X  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+9x^82+24x^83+34x^84+160x^85+26x^86+528x^87+18x^88+160x^89+26x^90+24x^91+8x^92+2x^94+1x^96+2x^100+1x^162

The gray image is a code over GF(2) with n=696, k=10 and d=328.
This code was found by Heurico 1.16 in 0.765 seconds.