The generator matrix

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

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+52x^84+156x^85+232x^86+200x^87+249x^88+196x^89+238x^90+112x^91+150x^92+72x^93+94x^94+64x^95+59x^96+40x^97+40x^98+20x^99+14x^100+16x^101+8x^102+4x^103+8x^104+16x^105+2x^106+2x^108+2x^110+1x^112

The gray image is a code over GF(2) with n=360, k=11 and d=168.
This code was found by Heurico 1.11 in 0.502 seconds.