The generator matrix

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

generates a code of length 82 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+451x^76+664x^78+886x^80+576x^82+564x^84+352x^86+307x^88+148x^90+105x^92+16x^94+13x^96+4x^98+8x^100+1x^104

The gray image is a code over GF(2) with n=328, k=12 and d=152.
This code was found by Heurico 1.16 in 1.61 seconds.