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

generates a code of length 92 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 88.

Homogenous weight enumerator: w(x)=1x^0+82x^88+32x^89+176x^90+96x^91+302x^92+96x^93+112x^94+32x^95+50x^96+32x^98+10x^100+2x^112+1x^128

The gray image is a code over GF(2) with n=736, k=10 and d=352.
This code was found by Heurico 1.16 in 0.718 seconds.