The generator matrix

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

generates a code of length 83 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+127x^78+243x^80+171x^82+183x^84+176x^86+67x^88+25x^90+12x^92+10x^94+5x^96+2x^102+1x^108+1x^134

The gray image is a code over GF(2) with n=332, k=10 and d=156.
This code was found by Heurico 1.16 in 0.377 seconds.