The generator matrix

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

generates a code of length 90 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+165x^84+920x^85+1310x^86+1714x^87+1765x^88+2008x^89+1816x^90+1762x^91+1234x^92+1234x^93+769x^94+718x^95+431x^96+248x^97+128x^98+84x^99+41x^100+6x^101+14x^102+8x^103+2x^107+2x^108+3x^110+1x^112

The gray image is a code over GF(2) with n=720, k=14 and d=336.
This code was found by Heurico 1.16 in 4.38 seconds.