The generator matrix

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

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+146x^84+148x^85+238x^86+144x^87+211x^88+112x^89+202x^90+116x^91+182x^92+92x^93+128x^94+112x^95+81x^96+32x^97+44x^98+12x^99+29x^100+2x^102+3x^104+4x^106+1x^108+4x^110+2x^114+1x^116+1x^124

The gray image is a code over GF(2) with n=360, k=11 and d=168.
This code was found by Heurico 1.16 in 0.848 seconds.