The generator matrix

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

generates a code of length 92 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 85.

Homogenous weight enumerator: w(x)=1x^0+246x^85+932x^86+1616x^87+2294x^88+2856x^89+3516x^90+3710x^91+3479x^92+3688x^93+3150x^94+2454x^95+1831x^96+1140x^97+787x^98+482x^99+265x^100+128x^101+86x^102+38x^103+29x^104+16x^105+8x^106+4x^108+6x^109+4x^111+1x^112+1x^114

The gray image is a code over GF(2) with n=736, k=15 and d=340.
This code was found by Heurico 1.16 in 15.1 seconds.