The generator matrix

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

generates a code of length 83 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+507x^76+1170x^78+1487x^80+1256x^82+1217x^84+886x^86+793x^88+468x^90+280x^92+76x^94+29x^96+16x^98+4x^100+2x^104

The gray image is a code over GF(2) with n=332, k=13 and d=152.
This code was found by Heurico 1.13 in 2.04 seconds.