The generator matrix

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

generates a code of length 82 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+125x^74+304x^75+508x^76+436x^77+562x^78+652x^79+651x^80+776x^81+718x^82+620x^83+482x^84+568x^85+400x^86+392x^87+294x^88+236x^89+215x^90+76x^91+85x^92+28x^93+20x^94+4x^95+22x^96+4x^97+6x^98+4x^100+2x^102+1x^108

The gray image is a code over GF(2) with n=328, k=13 and d=148.
This code was found by Heurico 1.16 in 5.04 seconds.