The generator matrix

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

generates a code of length 88 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+160x^81+804x^82+1818x^83+2241x^84+2866x^85+3463x^86+3732x^87+3451x^88+3792x^89+3029x^90+2710x^91+1804x^92+1260x^93+722x^94+404x^95+261x^96+120x^97+53x^98+20x^99+29x^100+10x^101+5x^102+4x^103+4x^104+4x^106+1x^112

The gray image is a code over GF(2) with n=704, k=15 and d=324.
This code was found by Heurico 1.16 in 14.3 seconds.