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

generates a code of length 93 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 90.

Homogenous weight enumerator: w(x)=1x^0+110x^90+160x^91+216x^92+192x^93+154x^94+56x^95+40x^96+24x^97+41x^98+8x^99+2x^100+8x^101+6x^102+5x^104+1x^130

The gray image is a code over GF(2) with n=744, k=10 and d=360.
This code was found by Heurico 1.16 in 0.625 seconds.