The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+252x^82+208x^83+616x^84+272x^85+478x^86+544x^87+458x^88+352x^89+425x^90+144x^91+248x^92+16x^93+58x^94+19x^96+2x^98+2x^120+1x^122

The gray image is a code over GF(2) with n=696, k=12 and d=328.
This code was found by Heurico 1.16 in 15.6 seconds.