The generator matrix

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

generates a code of length 84 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+62x^80+160x^82+94x^84+128x^86+32x^88+32x^90+1x^96+1x^100+1x^132

The gray image is a code over GF(2) with n=336, k=9 and d=160.
This code was found by Heurico 1.16 in 0.326 seconds.