The generator matrix

 1  0  0  1  1  1 X+2  X  1  1  1  1  X  2  X  0  1  1  1 X+2  1  1  0  X  X  1  1  1  1  2  1  1  0  0  1  1  2  2  1  X  2  1  1  1  1  X  2  1  1  1  1  0 X+2  X  1  1  1  1  1  1  1 X+2  1  1 X+2  1  1  1  1  1  1  1  2 X+2  1  1  1  1  1  1 X+2  X  1
 0  1  0  0  1 X+1  1  0 X+2  2  3 X+3  1  1  X  1  X X+1  X  1  1  3  1  0  1  X X+1  X X+3 X+2  2  0  1  1  0  3  2  1  1  1  X X+2 X+3  2 X+1  1  1 X+2  2 X+2 X+3  1  X  X  1  0  X X+2  3  0  2  1  1  0  1 X+1  3 X+1 X+1 X+3  X  3  2  0 X+2  1  1 X+2  X X+1  1  X  0
 0  0  1  1  1  2  3  1  3  X X+2  3 X+3  X  1 X+1 X+2  0  1 X+2  3  2 X+2  1  1 X+3 X+3  2 X+3  1  1  2  2 X+1  2 X+1  1  2  X  2  1  0  3 X+1  X X+3  1  1 X+3  X  X  X  1  1 X+3 X+2 X+3 X+2 X+2  1 X+2  0  2  3  X  2  X  X  X X+2  0  0  1  1  2  2  2  1 X+3 X+1 X+2 X+2  0
 0  0  0  X X+2  0 X+2 X+2 X+2  0  0 X+2 X+2  2  X  2  X X+2  0 X+2  0  X X+2  2  2  0 X+2  2  2  X  0 X+2 X+2  X  0  0  2  2  X  2  2  X  0  X  0  2  0  2 X+2  X  0 X+2 X+2 X+2  0 X+2  X  0  2  0  0  X X+2  X  2  0  0 X+2 X+2  X  0  2  X  2 X+2  2  0  X X+2  X  X  2  0
 0  0  0  0  2  0  2  2  2  2  2  0  0  2  0  2  2  0  2  0  0  2  2  2  0  0  2  0  2  2  0  0  0  0  2  0  2  0  2  2  0  2  2  0  0  0  0  0  2  0  2  0  0  2  2  2  0  0  0  2  0  0  2  2  2  2  0  0  2  2  0  0  2  0  0  2  2  0  0  0  2  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+95x^76+216x^77+300x^78+388x^79+390x^80+360x^81+353x^82+354x^83+293x^84+220x^85+230x^86+230x^87+190x^88+124x^89+67x^90+96x^91+74x^92+36x^93+34x^94+14x^95+10x^96+4x^97+7x^98+4x^99+1x^104+1x^106+2x^107+2x^108

The gray image is a code over GF(2) with n=332, k=12 and d=152.
This code was found by Heurico 1.16 in 1.3 seconds.