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

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+544x^76+1080x^78+1540x^80+1290x^82+1132x^84+966x^86+772x^88+466x^90+264x^92+90x^94+23x^96+12x^98+12x^100

The gray image is a code over GF(2) with n=332, k=13 and d=152.
This code was found by Heurico 1.16 in 20.7 seconds.