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 X^2  1  X  1  1  X  1 X^2 X^2  1
 0 X^2+2  0  0  0 X^2 X^2+2 X^2  0  0  0  0 X^2 X^2+2 X^2 X^2+2  0  0 X^2 X^2  2  0 X^2 X^2+2  2 X^2 X^2 X^2  2  2  0 X^2+2  2  0  2 X^2  0 X^2 X^2+2 X^2  2  2 X^2 X^2+2  0 X^2 X^2+2  2  2  0 X^2  2 X^2+2  2 X^2 X^2+2  0 X^2  2  2 X^2+2 X^2+2  0 X^2  0 X^2 X^2+2 X^2+2  2  0 X^2  2  0  2  2  0  2 X^2+2 X^2+2 X^2  2 X^2  2 X^2+2  2 X^2+2  0
 0  0 X^2+2  0 X^2 X^2 X^2+2  0 X^2  0  0 X^2+2 X^2 X^2+2  0  0  0 X^2 X^2  0  0 X^2  2 X^2  2  0  2 X^2+2 X^2 X^2  2 X^2+2  0 X^2+2  2  2 X^2 X^2+2 X^2  2  2  0 X^2+2 X^2+2 X^2+2  2  0 X^2+2 X^2  0  2  0 X^2+2 X^2+2 X^2+2  2 X^2+2 X^2 X^2+2  0  2  0  2 X^2  2 X^2+2  2 X^2+2 X^2 X^2  0  0 X^2+2 X^2  2  0 X^2+2 X^2  0  2 X^2  0 X^2+2  2 X^2+2 X^2  2
 0  0  0 X^2+2 X^2  0 X^2+2 X^2 X^2  0 X^2+2  0  0 X^2+2 X^2  0  2 X^2+2  2 X^2+2 X^2  0  2 X^2  0  0 X^2+2 X^2  2 X^2 X^2+2  0  2 X^2 X^2  0  2 X^2+2  2 X^2 X^2+2  0  2 X^2 X^2+2  0 X^2  2  2  2 X^2+2 X^2+2  0 X^2+2 X^2  0  2 X^2+2 X^2+2 X^2+2  0 X^2+2  2  2  0  0  2  2  0  0  0  2 X^2 X^2+2 X^2+2 X^2  2 X^2+2 X^2 X^2+2  0  2 X^2  2 X^2+2 X^2  2
 0  0  0  0  2  0  0  0  0  2  2  2  2  2  2  2  2  2  2  2  0  0  0  0  0  2  0  2  2  0  2  0  2  0  2  0  0  0  0  0  0  0  2  2  2  2  2  2  0  0  2  2  2  0  0  2  2  2  2  0  0  0  2  0  0  0  2  0  2  2  0  0  2  0  2  0  0  2  0  2  0  2  0  0  2  0  0

generates a code of length 87 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+112x^82+8x^83+145x^84+128x^85+398x^86+496x^87+395x^88+128x^89+130x^90+8x^91+57x^92+26x^94+8x^96+6x^98+1x^100+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 92.9 seconds.