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

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

Homogenous weight enumerator: w(x)=1x^0+42x^84+95x^86+32x^87+168x^88+96x^89+213x^90+96x^91+127x^92+32x^93+45x^94+43x^96+27x^98+2x^100+4x^102+1x^172

The gray image is a code over GF(2) with n=360, k=10 and d=168.
This code was found by Heurico 1.16 in 0.654 seconds.