The generator matrix

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

generates a code of length 87 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+92x^80+228x^81+353x^82+350x^83+334x^84+352x^85+332x^86+388x^87+310x^88+282x^89+244x^90+178x^91+143x^92+122x^93+131x^94+72x^95+70x^96+34x^97+17x^98+30x^99+7x^100+6x^101+6x^102+4x^103+3x^104+2x^106+2x^107+3x^110

The gray image is a code over GF(2) with n=348, k=12 and d=160.
This code was found by Heurico 1.16 in 1.42 seconds.