The generator matrix

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

generates a code of length 87 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+55x^74+12x^75+128x^76+70x^77+150x^78+130x^79+279x^80+294x^81+406x^82+410x^83+501x^84+692x^85+573x^86+860x^87+536x^88+708x^89+526x^90+456x^91+378x^92+230x^93+236x^94+162x^95+153x^96+54x^97+54x^98+18x^99+38x^100+27x^102+20x^104+15x^106+10x^108+5x^110+3x^112+1x^116+1x^126

The gray image is a code over GF(2) with n=348, k=13 and d=148.
This code was found by Heurico 1.16 in 9.56 seconds.